LYSYCHANSK, Ukraine — All of the bridges connecting the twin Ukrainian cities of Lysychansk and Sievierodonetsk are destroyed and street-by-street fighting is raging, leaving thousands of civilians largely trapped inside one of the deadliest battles of the war so far.

Russia has targeted the area since its full-scale invasion began in February, but as it has narrowed its offensive to the resource-rich eastern Donbas region, Russian commanders have steadily redirected more forces to the small pocket of land in and around Sievierodonetsk.

There are an estimated 10,000 people still in the city of Sievierodonetsk, with several hundred believed to be holed up in bunkers beneath a chemical plant that is under near constant bombardment. The Ukrainian government said this week that any large-scale evacuation of the city is now impossible. Russia has promised to create a humanitarian corridor, but previous claims have failed to materialize and Russian forces have directed their fire in locations where civilians were gathering to flee.

Fierce fighting continued on Thursday in Lysychansk and Sievierodonetsk. A Russian airstrike struck the center of Lysychansk on Thursday morning, killing at least one person, local authorities said.

Throughout most of the day, Russian and Ukrainian artillery fired from opposing banks of the Siversky Donets River, which divides the two towns. A group of Ukrainian soldiers, taking a breather from the fighting in the basement in a Soviet-style apartment, asked reporters from The New York Times when Western rocket artillery systems would arrive, and said they needed many of them.

On the front line as Russian artillery pounds the city of Lysychansk, “one hour feels like an entire day,” one soldier said.

In Sievierodonetsk, the people in the ruined city are now largely on their own. Those who have made it out recently describe harrowing scenes.

Serhiy Haidai, the head of the Luhansk military administration, said that the shelling was now so intense that “people can no longer stand it in the shelters — their psychological state is on the edge.”

Russia does not control the city, he said, and pitched battles are being fought from house to house. At the same time, Russian forces continue to lay waste to the villages around the city, Mr. Haidai said.

“The destruction of the residential sector is catastrophic,” he said. People in the city have reported running out of food and clean water — describing scenes similar to those that played out in Mariupol and many other towns and cities along the eastern front over the past four months.

Another 60,000 civilians are still believed to be living in Ukrainian-controlled Lysychansk. But the constant Russian bombardment of the area as Russia tries to encircle Ukrainian forces there has made any large-scale evacuation an exceedingly tough proposition.

Much of the estimated 50,000 to 60,000 rounds of artillery Russia is unleashing every day is concentrated in this last sliver of Luhansk Province under Ukrainian control.

The kind of convoy needed for a large-scale evacuation would most likely require coordination between Russia and Ukraine overseen by international mediators. There has been no public suggestion that such a plan is being discussed. In Lysychansk, volunteers, in a medley of vehicles, are evacuating dozens of civilians each day.

Ukraine’s top military commander, Valerii Zaluzhnyi, said in a statement that Russia had focused its efforts on this battle. In addition to nonstop artillery barrages, he said, Moscow is directing airstrikes and using multiple rocket launch systems to obliterate everything in its path. Russian forces are trying to advance along nine separate fronts from the north, east and south.

Despite Russia’s superior arsenal, the Ukrainians have been able to keep Moscow’s forces from completing the encirclement of the area. General Zaluzhnyi said they would continue to fight.

Sievierodonetsk, he said, is a key point in the defensive system of the Luhansk region. “The city can be seen as nothing less than that,” he said.

Volodymyr Titulenko has long been haunted by his early childhood memories of World War II. Now, at 82 years old, the artist is expressing his pain about the current war through his painting.

Mr. Titulenko’s home in the village of Rusaniv, an hour east of Kyiv, was on the front line between the Ukrainian military and the forces invading from Russia. With his wife and granddaughter in Kyiv making sure his work in a gallery there was safe, he spent two weeks sheltering in his village home alone.

Mr. Titulenko, who can see well out of only one eye, has been glued to television reports about the war, and that is reflected in his art.

After he returned to his studio in his flower-filled backyard, one of his first paintings was “Spring in Rusaniv,” which shows blossoming wildflowers in the foreground and flaming Russian tanks in the background. On the road near the tanks, the bodies of two Russian soldiers are splayed.

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The Russians have been trying to advance in eastern Ukraine for the past few weeks and have been pushing especially hard as Victory Day approaches, but Ukrainian forces — armed with new weapons supplied by the United States and other Western nations — have been pushing back in a counteroffensive.

The destruction of three bridges by Russian forces, about 12 miles northeast of Kharkiv, reported by the Ukrainian military, suggested that the Russians not only were trying to prevent the Ukrainians from pursuing them, but had no immediate plans to return.

A senior Ukrainian official, speaking on condition of anonymity to discuss the fighting, said Russian forces were destroying bridges not to retreat but because “we are pushing them out.”

He said the fight for Kharkiv was not over, and that although “at the moment we are dominating,” Russian forces were trying to regroup and go on the offensive.

Some military analysts said the Russian actions were similar to what Russia’s military had done last month in a retreat from the city of Chernihiv north of Kyiv.

Frederick W. Kagan, a military historian and a senior fellow at the American Enterprise Institute, a Washington-based public policy research group, said Russia’s strategy near Kharkiv could be an indicator that “the order to retreat to somewhere had been given and they were trying to set up a defensive line.”

Ukrainian forces have retaken a constellation of towns and villages in the outskirts of Kharkiv this past week, putting them in position to unseat Russian forces from the region and reclaim total control of the city “in a matter of days,” according to recent analysis by the Institute for the Study of War, a Washington-based research group.

The setback is now forcing the Russian military to choose whether to send reinforcements intended for elsewhere in eastern Ukraine to help defend the positions on the outskirts of Kharkiv, the institute said.

The back-and-forth around Kharkiv is part of a more complex battlefield in eastern Ukraine that has left an increasing number of towns and cities trapped in a “gray zone,” stuck between Russian and Ukrainian forces, where they are subject to frequent, sometimes indiscriminate, shelling.

“The Russian occupiers continue to destroy the civilian infrastructure of the Kharkiv region,” the region’s governor, Oleh Sinegubov, said in a Telegram post on Saturday, adding that shelling and artillery attacks overnight had targeted several districts, destroying a national museum in the village of Skovorodynivka.

For Russia, perhaps the best example of anything resembling a victory was the long-besieged southeastern port city of Mariupol. Although much of the city has been destroyed by Russian bombardments, there were growing indications on Saturday that Russia’s control of the city was nearly complete.

The Ukrainian Ministry of Defense’s intelligence directorate said in a Saturday statement that Russian officers were being moved from combat positions and sent to protect a Russian military parade being planned in Mariupol.

Petro Andrushchenko, an adviser to the city council, posted a series of photos to Telegram on Friday that appeared to show how Russian forces were restoring “monuments of the Soviet period” across the city.

One image appeared to show a Russian flag flying above an intensive care hospital. Another image, posted on Thursday, showed municipal workers replacing Ukrainian road signs with signs in Russian script. The images could not be verified.

On Friday, 50 people were evacuated from the city’s Azovstal steel plant, the final holdout of Ukrainian forces and a group of civilians in the city. Three Ukrainian soldiers were killed on Friday during an attempt to evacuate civilians from Mariupol’s Azovstal steel factory, said Mikhailo Vershinin, the chief of the city’s patrol police.

Mr. Vershinin, who was at the factory, said via a messaging app on Saturday that a rocket and a grenade were to blame. “Six were wounded, some seriously,” he said, and in the factory’s makeshift hospital, “there is no medicine, no anesthesia, no antibiotics and they may die.”

Both Ukrainian and Russian officials said Saturday that all civilian evacuations from the Mariupol factory had been completed.

There was no immediate confirmation from the Red Cross or United Nations, which have been helping to coordinate recent evacuations from the factory. A spokeswoman for the Red Cross said earlier on Saturday that efforts to evacuate the remaining civilians were “ongoing.”

Elsewhere, Russia launched six missile strikes on Saturday aimed at Odesa, Ukraine’s Black Sea port, according to the city council. Four hit a furniture company and destroyed two high-rise buildings in the blast, and two missiles were fired on the city’s airport, which already had been rendered inoperable by a Russian missile that knocked out its runway last week.

The goal of Russian forces — for now at least — appears to be seizing as much of the eastern Ukrainian region known as the Donbas as possible, by expelling Ukrainian forces that have been fighting Russian-backed separatists for years in the provinces of Donetsk and Luhansk. Since Russia’s invasion began on Feb. 24, about 80 percent of those two provinces have fallen under the Kremlin’s control.

The regional governor of Luhansk in eastern Ukraine, Serhiy Haidai, said on Facebook on Saturday that a Russian bomb hit a school in the village of Bilogorivka where about 90 people had taken shelter. About 30 people have been rescued so far, he said. The bodies of at least two people were recovered from the rubble, according to Ukraine’s State Emergency Service. Rescue operations were suspended on Saturday night and were to resume on Sunday, officials said.

Russian forces are trying to break through Ukrainian lines and encircle troops defending the area around the eastern city of Severodonetsk but are for now being held in check, the regional governor, Serhiy Haidai, said Saturday.

“It is a war so anything can happen, but for now the situation is difficult but under control,” Mr. Haidai said in a telephone interview. “They have broken through in some places and these areas are being reinforced.”

The Russians seemed “unlikely to successfully surround the town,” according to the latest update from the Institute for the Study of War.

The apparent aim of Russia’s military is to seize Severodonetsk or cut it off from the bulk of Ukrainian forces fighting in the east, and continue a push south to the major industrial city of Kramatorsk.

Mr. Haidai said Russia’s military had deployed units with better training and more combat experience than the Russian soldiers who were initially thrown into the invasion.

“In the beginning, they sent in newly-mobilized soldiers from occupied territory,” he said. “But they can’t fight. They aren’t dressed in flack jackets. And so they just died by the dozen or the hundred. But they’re running out of these.”

Mr. Haidai said he had urged anyone who could to evacuate, but that about 15,000 people remained in Severodonetsk. Some, he said, are older and “want to die in the place where they were born.”

By contrast in the capital, Kyiv, and much of the country’s west, the atmosphere seemed worlds away from the constant bombardment of the war — despite the occasional and unpredictable Russian missile strikes. Cars have returned to Kyiv’s streets and people living there have resumed some semblance of their normal routines.

In an apparent concern over complacency, President Volodymyr Zelensky reminded residents to heed local curfews and take air raid sirens seriously.

“Please, this is your life, the life of your children,” he implored Ukrainians in an overnight address.

Residents of towns and villages in the country’s east have often been shaken awake with bomb attacks, typically between 4 a.m. and 5 a.m.

On Saturday morning, the small village of Malotaranivka became a target. A bomb struck at about 4:15 a.m., blasting apart homes and a small bakery, leaving a crater at least 15 feet deep and a wide radius of destruction. While no one was killed, residents expressed fury at the Russians.

“What kind of military target is this?” said Tatyana Ostakhova, 38, speaking through the gaping hole in her goddaughter’s apartment where she was helping to clean up. “A store that bakes bread so people don’t die of hunger?”

Such strikes have occurred with more frequency in the prelude to Victory Day in Russia, which Mr. Putin was expected to use as a platform for some kind of announcement about what he has called the “special military operation” in Ukraine.

“It’s like we’re in a dream,” said Svetlana Golochenko, 43, who was cleaning up the remnants of her son’s house. “It’s hard to imagine that this is happening to us.”

Malotaranivka is a small village of single-family homes and wood-framed apartment buildings about eight miles from Kramatorsk. Residents said that aside from a few checkpoints there was no military presence in the area, making the bombings by Russians even more incomprehensible.

“Who knows what they have in their empty heads,” said Artur Serdyuk, 38, who was covered in dust and smoking a cigarette after spending the morning cleaning up what was left of his home.

Mr. Serdyuk said he had just returned to bed after going out for a middle-of-the-night cigarette when the explosion hit. The blast blew the roof off his home and incinerated his outhouse, leaving nothing but a roll of toilet paper sitting in a pile of dust near the hole for the latrine.

His neighbor’s home was opened like a dollhouse, allowing a reporter to peer into the remains of the kitchen decorated with wallpaper featuring green peacocks.

Michael Schwirtz reported from Sloviansk, and Cora Engelbrecht and Megan Specia reported from London. Ivan Nechepurenko contributed reporting from Tblisi, Georgia.

“He said, ‘Oleksandr Yurivich, you are looking at the map, you see the situation is predetermined,’” Mr. Vilkul said, recalling the conversation with a fellow minister in a former, pro-Russian Ukrainian government.

“Sign an agreement of friendship, cooperation and defense with Russia and they will have good relations with you,” the former colleague said. “You will be a big person in the new Ukraine.”

The offer failed spectacularly. Once war had begun, Mr. Vilkul said, the gray area seeped out of Ukrainian politics for him. Missiles striking his hometown made the choice obvious: He would fight back.

“I responded with profanity,” Mr. Vilkul said in an interview.

If the first months of the war in Ukraine became a military debacle for the Russian army — deflating the reputations of its commanders and troops in a forced retreat from Kyiv — the Russian invasion also highlighted another glaring failure: Moscow’s flawed analysis of the politics of the country it was attacking. The miscalculation led to mistakes no less costly in lives for the Russian army than the faulty tactics of tank operators who steered into bogs.

The Kremlin entered the war expecting a quick and painless victory, predicting that the government of President Volodymyr Zelensky would fracture and that leading officials in the largely Russian-speaking eastern region would gladly switch sides. That has not happened.

The political myopia was most significant in the country’s east, political analysts say.

In all but a tiny number of villages, Russia failed to flip local politicians to its side. The Ukrainian authorities have opened 38 cases of treason, all targeting low level officials in individual instances of betrayal.

“Nobody wanted to be part of that thing behind the wall,” said Kostyantyn Usov, a former member of Parliament from Kryvyi Rih, referring to Russia’s isolated, authoritarian system.

He said that system had dismal appeal in Ukraine and noted the absence of widespread collaboration with Russia, including among Ukrainians who speak Russian and share the country’s cultural values.

“We are part of something bright,” he said of Ukraine. “It is here, with us, in our group. And they have nothing to offer.”

Other prominent, once Russian-leaning politicians including Ihor Terekhov, the mayor of Kharkiv, and Hennady Trukhanov, the mayor of Odesa, also remained loyal and became fierce defenders of their cities.

Along with leaders in the southeast, Ukrainian people also resisted. Street protests against occupation in Kherson continue despite lethal dangers for participants. One man stood in front of a tank. Kryvyi Rih’s miners and steelworkers have shown no signs of pivoting allegiance to Russia.

“Before the war, we had ties to Russia,” said Serhiy Zhyhalov, 36, a steel mill engineer, referring to familial, linguistic and cultural bonds. But no longer, he said. “No one has any doubts that Russia attacked us.”

Ukraine’s southeastern regions, an expanse of steppe and blighted industrial and mining cities, is now the focus of fighting in the war.

Driving south from Kyiv, the highway leaves behind the dense pine forests and reedy swamps of northern Ukraine, and the landscape opens into expansive plains. Farm fields stretch out to the horizons, in brilliant, yellow blossoming rapeseed or tilled black earth.

In many ways, the region is entwined with Soviet and Russian history. The iron and coal industries shaped southeastern Ukraine. In and around the city of Kryvyi Rih are iron ore deposits; the coal is farther east, near the city of Donetsk.

The two mineral basins, known as the Kryvbas and the Donbas, gave birth to a metallurgical industry that drew in many nationalities from around the Czarist and Soviet empires from the late 19th century onward, with Russian becoming the lingua franca in the mining towns. Villages remained mostly Ukrainian speaking.

The region for years elected Russian-leaning politicians such as Mr. Vilkul, a favorite villain to Ukrainian nationalists for promoting Soviet-style cultural events that angered many Ukrainians. He staged, for example, a singalong party in Kryvyi Rih to belt out “Katyusha,” a Russian song associated with the Soviet World War II victory.

More substantively, Mr. Vilkul ascended in politics under the former, pro-Russian president, Viktor F. Yanukovych, in whose government he served as deputy prime minister until street protesters deposed Mr. Yanukovych in 2014.

Much of the rest of Mr. Yanukovych’s cabinet fled with him to Russia. But Mr. Vilkul remained in Ukraine as a de facto political boss of Kryvyi Rih while his aging father served as the city’s mayor.

And he caught Moscow’s eye. In 2018, Mr. Vilkul said in the interview, he was told through an intermediary that “the time of chaos is over” and that he should now follow orders from Moscow if he wished to remain in politics in the southeast. He said he refused.

The Russians, he said, had not even bothered to court him, they only leveled demands. He said Moscow took the same approach to other politicians in Ukraine’s east. “They didn’t even try to convince us,” he said. “They just thought we would be, a priori, on their side.”

On the eve of the war, Mr. Vilkul was most likely the Russian-leaning politician in Ukraine with the broadest popular support. “I was alone on this level,” he said. He was also viewed by Moscow as a promising potential convert to its side when it invaded Ukraine.

That’s when the call came to Mr. Vilkul’s cellphone from Vitaly Zakharchenko, a Ukrainian in exile in Russia who had served as interior minister under Mr. Vilkul in Mr. Yanukovych’s government. He recommended Mr. Vilkul cooperate with the Russians.

“I told him to get lost,” Mr. Vilkul said. “I didn’t even consider it.”

Mr. Vilkul said he had been misunderstood — by Russia’s leadership and his nationalist opposition at home. A great-grandfather, he said, had fought White Russians in the civil war. The Vilkul family, he said, “has been fighting Russians on this land for a hundred years.”

The Kremlin, he said, had misinterpreted his respect for World War II veterans and support for rights of Russian speakers as potential support for a renewed Russian empire, something he said was a mistake. He called the Russians “classic megalomaniacs.”

“They mistook common language and values like attitudes to the Second World War and Orthodoxy as a sign that somebody loves them,” he said.

A second offer, this time presented publicly by another Ukrainian exile, Oleh Tsaryov, in a post on Telegram, came about a week later, when Russian troops had advanced to within six miles of the city. “My fellow party members and I have always taken a pro-Russian stance,” the post said, referring to Mr. Vilkul and his father, and added ominously that “cooperation with the Russian army means preserving the city and lives.”

Mr. Vilkul responded with an obscene post on Facebook.

On the first days of the invasion, Mr. Vilkul ordered the region’s mining companies to park heavy equipment on the runway of the city’s airport, thwarting an airborne assault, and on approach roads, slowing tank columns. The tires were then popped and engines disabled.

The city’s steel industry began to turn out tank barriers and plates for armored vests. Mr. Zelensky, whose hometown is Kryvyi Rih, appointed Mr. Vilkul military governor of the city on the third day of the war, though the two had been political opponents in peacetime.

Mr. Vilkul has taken to wearing fatigues and a camouflage bandanna. A parade of Ukrainian nationalists, including the leader of the Right Sector paramilitary, Dmytro Yarosh, and a prominent activist and military officer, Tetiana Chernovol, once sworn enemies of the Vilkul family, have shown up in his office to shake his hand.

“If we fight the Russians,” he said, “were we ever really pro-Russian, in essence?”

Maria Varenikova contributed reporting.

Those who had been trapped in Mariupol outside the steel mill described a fragile existence, subsisting on Russian rations cooked outside on wood fires amid daily shelling that left corpses lying in debris.

Yelena Gibert, a psychologist who reached Ukrainian-held territory with her teenage son on Monday, described “hopelessness and despair” in Mariupol, and said residents were “starting to talk of suicide because they’re stuck in this situation.”

Heavy fighting in the eastern Donetsk and Luhansk regions has yielded minimal gains for the forces of President Vladimir V. Putin of Russia, Western officials say. But the Russians continued to fire rockets and shells at Ukrainian military positions, cities, towns and infrastructure along a 300-mile-long front, including bombarding the Azovstal plant, where the last remaining Ukrainian fighters in Mariupol are hunkered down.

On Monday, Ukraine said it had used Turkish-made drones to destroy two Russian patrol vessels off the Black Sea port of Odesa, just before Russian missiles struck the city, causing an unknown number of casualties and damage to a religious building.

The U.S. State Department said that Russia’s war aims now include annexing Donetsk and Luhansk — partially controlled before the Feb. 24 invasion by Russia-backed separatists — as soon as mid-May, and possibly the southern Kherson region as well.

“We believe that the Kremlin may try to hold sham referenda to try to add a veneer of democratic or electoral legitimacy, and this is straight out of the Kremlin’s playbook,” Michael Carpenter, the U.S. ambassador to the Organization for Security and Cooperation in Europe, told reporters at a State Department briefing in Washington.

As the war drags on and evidence of atrocities mounts, the West’s appetite has grown for retaliation that would have been rejected out of hand a few months ago. The U.S. Senate is preparing to take up President Biden’s $33 billion aid package for Ukraine, including a significant increase in heavy weaponry, and the European Union is expected this week to impose an embargo on Russian oil, a significant step for a bloc whose members have long depended on Russian energy.

House Speaker Nancy Pelosi, days after becoming the highest-ranking U.S. official to visit Kyiv since the war began, met in Warsaw with President Andrzej Duda of Poland on Monday, in an effort to strengthen Washington’s partnership with a key NATO ally that has absorbed millions of Ukrainian refugees and helped funnel arms to the battlefield.

Ms. Pelosi called for the “strongest possible military response, the strongest sanctions” to punish Russia for the invasion, despite Moscow’s threats of retaliation against the West. “They have already delivered on their threat that killed children and families, civilians and the rest,” she said.

More than two months into the invasion, Russia is struggling to capture and hold territory, according to a senior Pentagon official who briefed reporters on background to discuss intelligence. The official called Russia’s latest offensive in eastern Ukraine, the region known as Donbas, “very cautious, very tepid” and, in some cases, “anemic.”

“We see minimal progress at best,” the official said on Monday, citing incremental Russian advances in towns and villages. “They’ll move in, declare victory, then withdraw their troops, only to let the Ukrainians take it.”

Britain’s defense intelligence agency said that of the 120 battalion tactical groups Russia had used during the war — roughly 65 percent of its entire ground combat forces — more than a quarter had likely been “rendered combat ineffective.”

Some of Russia’s most elite units, including its Airborne Forces, have “suffered the highest levels of attrition,” the British assessment said, adding that it would “probably take years for Russia to reconstitute these forces.”

As the fighting raged in eastern and southern Ukraine, Moscow on Monday faced a growing diplomatic backlash after the Russian foreign minister, Sergey V. Lavrov, said that Jews were “the biggest antisemites.”

Mr. Lavrov made the remarks on Sunday to an Italian television journalist who had asked him why Russia claimed to be “denazifying” Ukraine when its president, Volodymyr Zelensky, was Jewish and members of his family had been killed in the Holocaust.

Mr. Lavrov replied that he thought Hitler himself had Jewish roots, a claim dismissed by historians, and added, “For a long time now we’ve been hearing the wise Jewish people say that the biggest antisemites are the Jews themselves.”

The Israeli Foreign Ministry summoned the Russian ambassador to Israel to explain Mr. Lavrov’s remarks, while Israel’s foreign minister, Yair Lapid, demanded an apology. The Israeli prime minister, Naftali Bennett, said of Mr. Lavrov’s remarks, “The goal of such lies is to accuse the Jews themselves of the most awful crimes in history, which were perpetrated against them.”

Senator Chuck Schumer, the majority leader and highest-ranking Jewish elected official in the United States, called Mr. Lavrov’s comments “disgusting.”

Those who escaped Mariupol and reached the southern city of Zaporizhzhia had managed to survive in a Russian-occupied city crushed by intense shelling, where Ukrainian officials say more than 20,000 civilians have been killed. About 20 civilians who were sheltering under the Azovstal mill got out of the city on Saturday, about 100 did so on Sunday and an unknown number followed on Monday.

Every morning at about 6 a.m., Ms. Gibert said, residents outside the plant lined up for rations handed out by Russian soldiers. First, they had to listen to the Russian national anthem and then to the anthem of the separatist Ukrainian region known as the Donetsk People’s Republic, she said.

A number was scrawled on the hand of each resident there, and then they waited, sometimes all day, to receive boxes of food, Ms. Gibert said. Inside a typical ration box was macaroni, rice, oatmeal, canned meat, sweet and condensed milk, sugar, butter. It was supposed to last a month, but didn’t always — especially when shared with a teenage boy, Ms. Gibert said.

In a city where many residential buildings have been destroyed and the remainder lacked power, heat or, much of the time, running water, Ms. Gibert said she and her son were among the lucky ones.

“Our apartment is still partially intact,” she said. “On one side, we have all our windows.”

Anastasiya Dembitskaya, 35, who reached Zaporizhzhia with her two children and a dog, said a drop in fighting in Mariupol over the past few weeks had allowed spotty telephone service to return and small markets to open, selling food from Russia and Russian-controlled Ukrainian territory at stratospheric prices.

“They’ve begun to at least remove the trash, which is good,” Ms. Dembitskaya said. “The bodies and the trash and the wires that were lying everywhere.”

Ksenia Safonova, who also arrived in Zaporizhzhia, said that she and her parents had wanted to leave Mariupol weeks ago but were pinned down by rocket fire.

“When we tried to leave, intense shelling started,” she said. “Everything was exploding. Jets were flying overhead and it was too scary to leave.”

When food became scarce, she said, her family relied on rations handed out by the Russian troops. She pulled out a can of preserved meat that she said was part of a Russian humanitarian aid package. Its expiration date was Jan. 31, nearly a month before the invasion began.

Ms. Safonova and her family were finally able to leave Mariupol on April 26 in a minibus with six other people. At checkpoints on the way to Zaporizhzhia, she said, Russian soldiers insulted her and her family, warning that Ukrainian forces would not welcome them and might shell them when they arrived.

Once, she said, the soldiers tried to trick them into revealing their loyalty to Ukraine.

“At one checkpoint they yelled ‘Glory to Ukraine,’ to see whether we would yell, ‘Glory to the heroes,’ though, of course, we knew that would end badly,” she said, referring to a patriotic greeting among Ukrainians that has become widespread during the war.

“We still know truth is on our side,” she said.

Michael Schwirtz reported from Zaporizhzhia, Ukraine, and Michael Levenson from New York. Reporting was contributed by Lara Jakes and Eric Schmitt from Washington, Myra Noveck from Jerusalem, Marc Santora from Krakow, Poland, Monika Pronczuk from Brussels and Matthew Mpoke Bigg from London.