PRUDYANKA, Ukraine — Ukrainian troops sat on a bench under the trees cracking jokes. One hopped on a bicycle and cycled off down the empty road. This was the safest part of Prudyanka, a village north of the city of Kharkiv, their commander said with a cheerful laugh.

Ukrainian soldiers are in good spirits in this northeastern region of Ukraine. They were part of a Ukrainian counterattack force that successfully pushed Russian troops back from Kharkiv two weeks ago, putting an end to months of shelling of the city, Ukraine’s second-largest.

In the ensuing euphoria over dealing that setback to the Russian forces, there was talk of Ukrainian troops marching on to the Russian border only 25 miles away. But that seems to have been premature, with some Russian troops north of Kharkiv holding on and digging in, becoming much harder to drive back.

While the Russians did withdraw from the immediate outskirts of Kharkiv, they are still close enough to shell the city and heavy fighting continues within earshot of a ring of villages to the east that they recently abandoned, Ukrainian troops and villagers said in interviews.

“We are afraid they will come again,” said Olha, 66, who was collecting freshly laid eggs in her village of Vilkhivka, east of Kharkiv, as the bombardment sounded from across the hills. “God help us that it does not happen.”

In recent days, both armies have traded artillery fire across the tree lined hills that roll away north and east of the city. On Thursday, black smoke rose on the horizon over several locations in Russian-held territory.

Not surprisingly, the Ukrainian forces remain confident they will rout the Russians eventually.

“They will lose their ability to fight the war,” said Vitaliy Chorny, a member of a volunteer brigade who works as a forward spotter, flying drones to identify targets for Ukrainian artillery units. “Our guys are not feeling tired and they are the opposite.” But the Ukrainians also say they are encountering tough resistance from Russian units that have constructed extensive defensive positions.

“There is a whole underground city there,” one officer said, gesturing further north. He gave only his code name, Tikhi, and his age, 31, according to military protocol. “They have trenches, bunkers, everything is operating underground. We tried one time to take it. It was quite scary.”

The city of Kharkiv is springing back to life, with 2,000 people returning daily by train, cafes opening and public buses returning to service Monday for the first time since February.

“We consider that we have been successful and they lost, in fact,” Oleh Synyehubov, the governor of Kharkiv, said. He gave an interview in the street under the trees as his office on Kharkiv’s central square was gutted by direct hits from two cruise missiles in March.

Yet a tour through the villages north and east of the city revealed a more precarious situation.

As they retreated, the Russians abandoned dozens of their own dead, amid burned out tanks and armor and smashed trenches across the undulating hills. Few people have returned to the battered areas. A dead Russian soldier still lay on the grounds of a burned out school in Vilkhivka, his chest bare, his body swollen and blackened.

A villager, Nikolai, 62, was pushing a damaged cart he said he had used to carry the body of a local person to the graveyard. Almost too distraught to speak, he began to weep. “Nobody thought it would be so,” he said wiping his eyes. “All the houses around me burned.”

The Russian forces, stalled around Kharkiv since the early weeks of the invasion, were reinforced with troops withdrawn from Kyiv after the Russian drive there was defeated, Mr. Chorny said.

“They were digging in,” he said of the Russians. “They were well prepared, serious soldiers. They had brand-new tanks and good equipment, which is proof that they thought the area was strategically important.”

Ukrainian forces, also freed up from Kyiv, piled into the region at the same time. Mr. Chorny was part of a group that harried the Russians as they withdrew from towns and villages east of Kyiv before taking part in the counterattack in Kharkiv.

But as that drive was pushing ahead — and just after his unit had suffered a painful battlefield reversal — the Russians abandoned their positions.

Exactly why they retreated became clear, he said, when he went back to survey the battlefield last week and was stunned by the extent of the destruction to the Russian positions wrought by Ukrainian artillery. “I cannot even believe how hard it was for them,” he said. “It was impossible for them to hold.”

In response to urgent appeals from Kyiv, several European countries have sent tanks and heavier guns to Ukraine recently, while the U.S. has shipped 90 long-range, M777 howitzers that are already in action along the 300-mile-long frontline in the east.

It remains unclear, however, what role Western shipments of long-range howitzers and other heavy weapons played in the counterattack in Kharkiv.

Mr. Chorny said he had not seen any of the new howitzers in use there but that they had been employed elsewhere in the region. The howitzers reportedly played a part in another disastrous episode for Russian forces on May 11, when hundreds of soldiers were killed attempting a river crossing at Bilohorivka in the eastern region of Luhansk.

But in Kharkiv, as well as in Kyiv before that, the Ukrainian troops relied mostly on the agility of their forward spotters and the responsiveness and effectiveness of their artillery units.

Much has been written about shoulder-held anti-tank missiles supplied by the West to Ukrainian forces, but the greatest damage done to the advancing Russian columns was by Ukrainian artillery, guided by Ukrainian special forces troops and spotters using drones, analysts with the Royal United Services Institute in London said in a recent report.

In both cities, the Russian forces were hampered by poor logistics, faulty planning and open communications channels that alerted the Ukrainians to their movements, the analysts said. The Ukrainians, by contrast, had the advantage of the local population as its eyes and ears who called in with sightings of Russian troops.

The Russian army has rarely had to face a country with such strong artillery, tank and rocket divisions, Mr. Chorny said. “They were hit every day,” he said. “Every day we were killing them, with hundreds of high caliber artillery shells flying at them, and thanks to our help, those hits were very precise.”

Yet despite such successes, Ukrainian soldiers and officers are still confronting the brunt of Russian firepower throughout the eastern provinces of Luhansk and Donetsk, known collectively as the Donbas.

In fact, Mr. Chorny conceded, Ukrainian units were likely to lose ground further south and east in the Donbas, where Russian forces are now concentrating their efforts.

And fighting is still heavy in the Kharkiv region. Mourners at two military funerals taking place in Kharkiv on Thursday said the men’s battalion had suffered eight dead and 40 wounded just this week.

A 49-year-old businessman who enlisted at the beginning of the war and goes by the code name of Odin, was nursing wounds to his face from a mine blast just north of Kharkiv in an area recently vacated by the Russians. One of his soldiers lost a leg in the blast, he said.

The first forces that came into Ukraine in February and March were mostly ill-prepared and inexperienced, Odin said. But the units now being deployed are better trained and more experienced, he added.

“It is getting much more difficult,” he said. “They are digging in and now we are facing a competent army.”

The soldiers at the frontline village of Prudyanka had been unable to advance for three weeks, the officer code-named Tikhi said, because they lacked the necessary artillery support against the well dug in Russian troops.

But he was also derisive about the enemy. “They are firing from left and right and in front of us,” he said. “Sometimes we are laughing because they are firing on each other.”

As his radio crackled into life, he said there were ethnic conflicts between some of the Russian units, which included men from Dagestan in the Caucasus and Buryatis from Russia’s Far East, near the Chinese border.

“God is helping us,” he said. “They are firing on each other, stupid bastards.”