Nearly every U.S. state has now announced plans for when all adult residents will be eligible to be vaccinated — meeting, and in some cases, beating, President Biden’s target date of April 19.

The U.S. vaccination campaign has steadily picked up pace: More than three million doses are being given on average each day, compared with well under one million when Mr. Biden took office in January, according to the Centers for Disease Control and Prevention. Every state has now given at least one dose to a quarter or more of its population. About 62.4 million people — 19 percent of Americans — have been fully vaccinated.

“Today, we are pleased to announce another acceleration of the vaccine eligibility phases to earlier than anticipated,” Gov. Larry Hogan of Maryland said on Monday, announcing that all Maryland residents 16 or older would be eligible from Tuesday for a vaccine at the state’s mass vaccination sites, and from April 19 at any vaccine provider in the state.

Also on Monday, Gov. Philip D. Murphy of New Jersey said residents 16 or older in his state would be eligible on April 19. Mayor Muriel Bowser of Washington said later on Monday that city residents 16 or older would also be eligible on April 19.

That leaves two states, Oregon and Hawaii, keeping to Mr. Biden’s original deadline of May 1. Their governors did not immediately respond to requests for comment about whether they would broaden eligibility sooner, but Gov. Kate Brown of Oregon announced on Monday that all frontline workers and their families, as well as those 16 or older with underlying health conditions, would be eligible immediately.

In Hawaii, 34 percent of residents have received at least one dose; in Oregon, the figure is 31 percent. Alabama has vaccinated the lowest proportion of its residents, at 25 percent.

But as Ms. Brown noted in her announcement about eligibility — and as experts have warned for weeks — “we’re in a race between vaccines and variants.”

Along with dangerous coronavirus variants that were identified in Britain, South Africa and Brazil, new mutations have continued to pop up in the United States, from California to New York to Oregon.

The shots will eventually win, scientists say, but because each infection gives the coronavirus a chance to evolve further, vaccinations must proceed as fast as possible.

As that race continues, the optimism sown by the steady pace of vaccinations may be threatening to undermine the progress the nation has made. Scientists also fear Americans could let their guard down too soon as warmer weather draws them outside and case levels drop far below the devastating surge this winter.

Cases are now rising sharply in parts of the country, with some states offering a stark reminder that the pandemic is far from over: New cases in Michigan have increased 112 percent and hospitalizations have increased 108 percent over the past two weeks, according to a New York Times database.

The United States is averaging more than 64,000 new cases each day, an 18 percent increase from two weeks earlier. That’s well below the peak of more than 250,000 new cases daily in January, but on par with last summer’s surge after reopenings in some states, like Arizona, where patrons packed into clubs as hospital beds filled up. The United States is averaging more than 800 Covid-19 deaths each day, the lowest level since November.

Yet again, governors across the country have lifted precautions like mask mandates and capacity limits on businesses. Medical experts have warned that these moves are premature, and Mr. Biden has urged governors to reinstate the restrictions.

Travel is up again, too, with more than one million people passing through airport security each day in the United States since March 11, according to the Transportation Security Administration. On Sunday, more than 1.5 million people passed through T.S.A. checkpoints. The C.D.C. said last week that fully vaccinated Americans could travel domestically with low risk, but should still follow precautions like wearing masks.

In Beijing, the vaccinated qualify for buy-one-get-one-free ice cream cones. In the northern province of Gansu, a county government published a 20-stanza poem extolling the virtues of the jab. In the southern town of Wancheng, officials warned parents that if they refused to get vaccinated, their children’s schooling and future employment and housing were all at risk.

China is deploying a medley of tactics, some tantalizing and some threatening, to achieve mass vaccination on a staggering scale: a goal of 560 million people, or 40 percent of its population, by the end of June.

China has already proven how effectively it can mobilize against the coronavirus. And other countries have achieved widespread vaccination, albeit in much smaller populations.

But China faces a number of challenges. The country’s near-total control over the coronavirus has left many residents feeling little urgency to get vaccinated. Some are wary of China’s history of vaccine-related scandals, a fear that the lack of transparency around Chinese coronavirus vaccines has done little to assuage. Then there is the sheer size of the population to be inoculated.

To get it done, the government has turned to a familiar tool kit: a sprawling, quickly mobilized bureaucracy and its sometimes heavy-handed approach. This top-down, all-out response helped tame the virus early on, and now the authorities hope to replicate that success with vaccinations.

Already, uptake has skyrocketed. Over the past week, China has administered an average of about 4.8 million doses a day, up from about one million a day for much of last month. Experts have said they hope to reach 10 million a day to meet the June goal.

“They say it’s voluntary, but if you don’t get the vaccine, they’ll just keep calling you,” said Annie Chen, a university student in Beijing who received two such entreaties from a school counselor in about a week.

A top vaccines official at the European Medicines Agency said on Tuesday that AstraZeneca’s vaccine was linked to blood clots in a small number of recipients, the first indication from a leading regulatory body that the clots may be a real, if extremely rare, side effect of the shot.

The agency itself has not formally changed its guidance, issued last week, that the benefits of the AstraZeneca vaccine outweigh the risks, but any further ruling from regulators would be a setback for a shot that Europe and much of the world are relying on to save lives amid a global surge in coronavirus cases.

The medicines agency said last week that no causal link between the vaccine and rare blood clots had been proven. Only a few dozen cases of blood clots have been recorded among the many millions of people who have received the vaccine across Europe.

But the vaccines official, Marco Cavaleri, told an Italian newspaper that “it is clear there is an association with the vaccine,” and that the medicines agency would announce “in the next hours” that it had determined there was a link. The medicines agency did not immediately respond to questions about its plans.

Those comments represented the first indication by a leading regulatory body that the blood clots could be a genuine, if extremely rare, side effect of the AstraZeneca vaccine. Previously, health officials in several European countries temporarily restricted the use of the shot in certain age groups, despite the European Medicines Agency’s recommendation to keep administering it.

Regulators in Britain and at the World Health Organization have also said that, while they were investigating any rare side effects, the shot was safe to use and would save many lives.

Mr. Cavaleri told the Italian newspaper Il Messaggero that European regulators had not determined why the vaccine might be causing the rare blood clots, which generated concern because the cases were so unusual. They involved blood clots combined with unusually low levels of platelets, a disorder that can lead to heavy bleeding.

The most worrisome of the conditions, known as cerebral venous sinus thrombosis, involves clots in the veins that drain blood from the brain, a condition that can lead to a rare type of stroke.

The clots are, by all accounts, extremely rare. European regulators were analyzing 44 cases of cerebral venous sinus thrombosis, 14 of them fatal, among 9.2 million people who received the AstraZeneca vaccine across the continent. Emer Cooke, the European Medicines Agency’s director, said that the clotting cases in younger people translated to a risk for one in every 100,000 people under 60 given the vaccine. Younger people, and especially younger women, are at higher risk from the brain clots, scientists have said.

In Britain, regulators last week reported 30 cases of the rare blood clots combined with low platelets among 18 million people given the AstraZeneca vaccine, which was developed with the University of Oxford. No such cases were reported in people who had received the Pfizer-BioNTech vaccine in Britain.

Regulators in Britain have said that people should get the vaccine “when invited to do so.” But British news reports indicated Monday night that regulators were considering updating that guidance for certain age groups.

Monika Pronczuk and Emma Bubola contributed reporting.

North Korea said on Tuesday that it had decided not to participate in the Tokyo Olympic Games this summer because of the coronavirus pandemic.

The North’s national Olympic Committee decided at a March 25 meeting that its delegation would skip the Olympics “in order to protect our athletes from the global health crisis caused by the malicious virus infection,” according to Sports in the Democratic People’s Republic of Korea, a government-run website.

It is the first Summer Olympics that the North has missed since 1988, when they were held in Seoul, the South Korean capital.

North Korea, which has a decrepit public health system, has taken stringent measures against the virus since early last year, including shutting its borders. The country officially maintains that it has no virus cases, but outside health experts are skeptical.

North Korea’s decision deprives South Korea and other nations of a rare opportunity to establish official contact with the isolated country. Officials in the South had hoped that the Olympics — to be held from July 23 to Aug. 8 — might provide a venue for senior delegates from both Koreas to discuss issues beyond sports.

The 2018 Winter Olympics, held in the South Korean city of Pyeongchang, offered similar hope for easing tensions on the Korean Peninsula. Kim Yo-jong, the only sister of North Korea’s leader, Kim Jong-un, grabbed global attention when she attended the opening ceremony, becoming the first member of the Kim family to cross the border into South Korea.

Mr. Kim used the North’s participation in the Pyeongchang Olympics as a signal to start diplomacy after a series of nuclear and long-range missile tests. Inter-Korean dialogue soon followed, leading to three summit meetings between Mr. Kim and President Moon Jae-in of South Korea. Mr. Kim also met three times with President Donald J. Trump.

But since the collapse of Mr. Kim’s diplomacy with Mr. Trump in 2019, North Korea has shunned official contact with South Korea or the United States. The pandemic has deepened the North’s diplomatic isolation and economic difficulties amid concerns over its nuclear ambitions. North Korea launched two ballistic missiles on March 25 in its first such test in a year, in a challenge to President Biden.

Since North Korea’s first Olympic appearance in 1972, it has participated in every Summer Games except for the Los Angeles event in 1984, when it joined a Soviet-led boycott, and in 1988, when South Korea played host. North Korean athletes have won 16 gold medals, mostly in weight lifting, wrestling, gymnastics, boxing and judo, consistently citing the ruling Kim family as inspiration.

The Tokyo Games were originally scheduled for 2020 but were delayed by a year because of the pandemic. The organizing committee has been scrambling to develop safety protocols to protect both participants and local residents. But as a series of health, economic and political challenges have arisen, large majorities in Japan now say in polls that the Games should not be held this summer.

Even though organizers have barred international spectators, epidemiologists warn the Olympics could still become a superspreader event. Thousands of athletes and other participants will descend on Tokyo from more than 200 countries while much of the Japanese public remains unvaccinated.

Prime Minister Jacinda Ardern of New Zealand announced on Tuesday that her nation would establish a travel bubble with Australia, allowing travelers to move between the countries without needing to quarantine for the first time since the pandemic began.

The bubble, which will open just before midnight on April 19, is expected to deliver a boost to tourism and to families that have been separated since both countries enacted strict border closures and lockdown measures that have all but eliminated local transmission of the coronavirus.

The announcement came after months of negotiations and setbacks, as Australia battled small outbreaks and officials in both countries weighed testing requirements and other safety protocols.

“The director general of health considers the risk of transmission of Covid-19 from Australia to New Zealand is low and that quarantine-free travel is safe to commence,” Ms. Ardern said at a news conference.

Since last year, Australia has permitted travelers from New Zealand to bypass its hotel quarantine requirements. New Zealand’s decision to reciprocate makes the two countries among the first places in the world to set up such a bubble, following a similar announcement last week by Taiwan and the Pacific island nation of Palau.

Australians flying to New Zealand will be required to have spent the previous 14 days in Australia, to wear a mask on the plane and, if possible, to use New Zealand’s Covid-19 contact tracing app. In the event of an outbreak in Australia, New Zealand could impose additional restrictions, including shutting down travel to a particular Australian state or imposing quarantine requirements, Ms. Ardern said.

She warned that the new requirements would not necessarily free up many spaces in New Zealand’s overwhelmed hotel quarantine system, which has a weekslong backlog for New Zealanders wishing to book a space to return home. Of the roughly 1,000 slots that would now become available every two weeks, around half would be set aside as a contingency measure, while most of the others would not be appropriate for travelers from higher-risk countries, Ms. Ardern said.

Before New Zealand closed its borders to international visitors in March 2020, its tourism industry employed nearly 230,000 people and contributed 41.9 billion New Zealand dollars ($30.2 billion) to economic output, according to the country’s tourism board. Most of the roughly 3.8 million foreign tourists who visited New Zealand over a 12-month period between 2018 and 2019 came from Australia.

Ms. Ardern encouraged Australians to visit New Zealand’s ski areas, and said she would be conducting interviews with Australian media outlets this week to promote New Zealand as a tourism destination.

The bubble would also make it easier for the more than 500,000 New Zealanders who live in Australia to visit their families.

“It is ultimately a change of scene that so many have been looking for,” Ms. Ardern said, addressing Australians. “You may not have been in long periods of lockdown, but you haven’t had the option. Now you have the option, come and see us.”

There was no need to pipe in crowd noise at Globe Life Field on Monday, as the Texas Rangers hosted the Toronto Blue Jays in front of the largest crowd at a sporting event in the United States in more than a year.

From the long lines of fans waiting to get into the stadium to the persistent buzz of the spectators during quiet moments, the game in Arlington, Texas, was a throwback to a time before the coronavirus crippled the country.

“It felt like a real game,” Rangers Manager Chris Woodward said. “It felt like back to the old days when we had full capacity.”

The official crowd of 38,238 fans, which was announced as a sellout, represented 94.8 percent of the stadium’s 40,300-seat capacity. It topped the Daytona 500 (which allowed slightly more than 30,000 fans) and the Super Bowl (24,835), both of which were held in February, as the largest crowd at a U.S. sporting event since the pandemic began last year.

The lifting of capacity restrictions in Texas made the enormous crowd possible. And for Major League Baseball, which claims its teams collectively lost billions during a largely fanless 2020 season, it was a hopeful sign that large crowds can return to all of the league’s games before too long. The open question is whether such events can be safe as the pandemic continues.

M.L.B. requires all fans over age 2 to wear masks at games this season, but a large percentage of the fans in Arlington went maskless. That will undoubtedly raise fears of the event resulting in a spike in coronavirus cases.

Garment workers in factories producing clothes and shoes for companies like Nike, Walmart and Benetton have seen their jobs disappear in the past 12 months, as major brands in the United States and Europe canceled or refused to pay for orders after the pandemic took hold and suppliers resorted to mass layoffs or closures.

Most garment workers earn chronically low wages, and few have any savings. Which means the only thing standing between them and dire poverty are legally mandated severance benefits that are often owed upon termination, wherever the workers are in the world.

According to a new report from the Worker Rights Consortium, however, garment workers are being denied some or all of these wages.

The study identified 31 export garment factories in nine countries where, the authors concluded, a total of 37,637 workers who were laid off did not receive the full severance pay they legally earned, a collective $39.8 million.

According to Scott Nova, the group’s executive director, the report covers only about 10 percent of global garment factory closures with mass layoffs in the last year. The group is investigating an additional 210 factories in 18 countries, leading the authors to estimate that the final data set will detail 213 factories with severance pay violations affecting more than 160,000 workers owed $171.5 million.

“Severance wage theft has been a longstanding problem in the garment industry, but the scope has dramatically increased in the last year,” Mr. Nova said. He added that the figures were likely to rise as economic aftershocks related to the pandemic continued to unfold across the retail industry. He believes the lost earnings could total between $500 million and $850 million.

The report’s authors say the only realistic solution to the crisis would be the creation of a so-called severance guarantee fund. The initiative, devised in conjunction with 220 unions and other labor rights organizations, would be financed by mandatory payments from signatory brands that could then be leveraged in cases of large-scale nonpayment of severance by a factory or supplier.

Several household names implicated in the report made money during the pandemic. Amazon, for example, reported an increase in net profit of 84 percent in 2020, while Inditex, the parent company of Zara, made 11.4 billion euros, about $13.4 billion, in gross profit. Nike, Next and Walmart all also had healthy earnings.

Some industry experts believe the purchasing practices of the industry’s power players are a major contributor to the severance pay crisis. The overwhelming majority of fashion retailers do not own their own production facilities, instead contracting with factories in countries where labor is cheap. The brands dictate prices, often squeezing suppliers to offer more for less, and can shift sourcing locations at will. Factory owners in developing countries say they are forced to operate on minimal margins, with few able to afford better worker wages or investments in safety and severance.

“The onus falls on the supplier,” said Genevieve LeBaron, a professor at the University of Sheffield in England who focuses on international labor standards. “But there is a reason the spotlight keeps falling on larger actors further up the supply chain. Their behavior can impact the ability of factories to deliver on their responsibilities.”

More than a year after the pandemic brought down the curtain at theaters and concert halls around the world, the performing arts are beginning to return to the stage.

A smattering of theater and comedy shows lit up New York stages over the last few days, but next week will see one of the higher-profile arts returns. The New York Philharmonic is scheduled to give its first live performance in a concert hall since the pandemic began: “a musical musing on Goethe,” at the Shed at the Hudson Yards development on April 14.

The reopenings come at a confusing moment in the pandemic. Vaccinations are rising in the United States — Saturday was the first time the country reported more than four million doses in a single day, according to data compiled by The New York Times — but so are case counts.

While new cases, deaths and hospitalizations are far below their January peak, the average number of new reported cases has risen 19 percent over the past two weeks.

Still, performance spaces are carefully starting to welcome audiences, at a fraction of their capacity. There remains much debate over what regulations to impose on attendees. In Israel, concertgoers are required to have a Green Pass, which certifies that they have been vaccinated, though enforcement can be spotty.

In New York, as at the Daryl Roth Theater, an Off Broadway venue, temperatures were checked as a small audience streamed in for an immersive sound performance based on the José Saramago novel “Blindness” — a dystopian tale from 25 years ago whose resonances eerily align with the present. Mayor Bill de Blasio, masked and sneaker-clad, greeted some theatergoers on the sidewalk outside with wrist and elbow bumps.

But that optimism has been tinged with more halting news that underscores how fragile these reopenings are.

The Park Avenue Armory had to postpone one of the most high-profile experiments to bring indoor live performance back to New York. A sold-out run of “Afterwardsness,” a new piece that addresses the pandemic and violence against Black people, was canceled after several members of the Bill T. Jones/Arnie Zane Company tested positive for the virus.

At the Comedy Cellar, a Greenwich Village club that has nursed the early careers of many comics, laughter filled the room for its first show, but reminders of reality were impossible to miss: Performers’ microphones were swapped out between each set, every fresh one covered with what looked like a miniature shower cap.

John Touhey, 27, said that his reason for coming was simple. “Just to feel something again,” he said.California officials have announced guidelines for indoor concerts, theater, sports and other events, which will be permitted beginning April 15. Capacity will be linked to a county’s health tier.

Los Angeles County, for example, on Monday moved into the orange tier, which would allow venues that hold up to 1,500 people to operate at 15 percent capacity, or 200 people. The number rises to 35 percent if all attendees are tested or show proof of vaccination.

In Minneapolis, pandemic-weary music fans may have to wait longer, but the results will be louder. First Avenue, a legendary club, last month booked its first new, non-postponed show since the pandemic began, The Star Tribune reported. The band is Dinosaur Jr., led by J. Mascis, one of the most durable indie rockers of the last 30 years. The show is scheduled for Sept. 14.

Minority communities in Britain have long felt estranged from the government and medical establishment, but their sense of alienation is suddenly proving more costly than ever amid a coronavirus vaccination campaign that depends heavily on trust.

With Britons enjoying one of the fastest vaccination rollouts in the world, skepticism about the shots remains high in many of the communities where Covid-19 has taken the heaviest toll.

“The government’s response to the Black, Asian and minority ethnic communities has been rather limited,” said Dr. Raja Amjid Riaz, 52, a surgeon who is also a leader at the Central Mosque of Brent, an ethnically diverse area of North London. “Those people have not been catered for.”

As a result, communities like Brent offer fertile ground for the most outlandish of vaccine rumors, from unfounded claims that they affect fertility to the outright fabrication that shots are being used to inject microchips.

With the government seen as still disengaged in Black, Asian and other ethnic minority communities even as they have been hit disproportionately hard both by the virus itself and by the lockdowns imposed to stop its spread, many local leaders like Dr. Riaz have taken it upon themselves to act.

Some are well-known and trusted figures like religious leaders. Others are local health care workers. And still others are ordinary community members like Umit Jani, a 46-year-old Brent resident.

Mr. Jani’s face is one of many featured on 150 posters across the borough encouraging residents to get tested for the virus and vaccinated, part of a local government initiative.

The goal is to reframe the community’s relationship with the power structure, and perhaps establish some trust.

“In Brent, things have been done to communities and not in partnership,” said Mr. Jani, who said he had seen the toll the virus has taken on the area’s Gujarati and Somali communities.

For most Americans, the third stimulus payment, like the first two, arrived as if by magic, landing unprompted in the bank or in the mail.

But it’s not as straightforward for people without a bank account or a mailing address. Or a phone. Or identification.

Just about anyone with a Social Security number who is not someone else’s dependent and who earns less than $75,000 is entitled to the stimulus. But some of the people who would benefit most from the money are having the hardest time getting their hands on it.

“There’s this great intention to lift people out of poverty more and give them support, and all of that’s wonderful,” said Beth Hofmeister, a lawyer for the Legal Aid Society’s Homeless Rights Project. “But the way people have to access it doesn’t really fit with how most really low-income people are interacting with the government.”

Interviews with homeless people in New York City over the last couple of weeks found that some mistakenly assumed they were ineligible for the stimulus. Others said that bureaucratic hurdles, complicated by limited phone or internet access, were insurmountable.

Paradoxically, the very poor are the most likely to pump stimulus money right back into devastated local economies, rather than sock it away in the bank or use it to play the stock market.

“I’d find a permanent place to stay, some food, clothing, a nice shower, a nice bed,” said Richard Rodriguez, 43, waiting for lunch outside the Bowery Mission last month. “I haven’t had a nice bed for a year.”

Mr. Rodriguez said he had made several attempts to file taxes — a necessary step for those not yet in the system — but had given up.

“I went to H&R Block and I told them I was homeless,” he said. “They said they couldn’t help me.”

U.S. coronavirus cases have increased again after hitting a low late last month, and some of the states driving the upward trend have also been hit hardest by variants, according to an analysis of data from Helix, a lab testing company.

The country’s vaccine rollout has sped up since the first doses were administered in December, recently reaching a rolling average of more than three million doses per day. And new U.S. cases trended steeply downward in the first quarter of the year, falling almost 80 percent from mid-January through the end of March.

But during that period, states also rolled back virus control measures, and now mobility data shows a rise in people socializing and traveling. Amid all this, more contagious variants have been gaining a foothold, and new cases are almost 20 percent higher than they were at the lowest point in March.

“It is a pretty complex situation, because behavior is changing, but you’ve also got this change in the virus itself at the same time,” said Emily Martin, an epidemiologist at the University of Michigan School of Public Health.

Michigan has seen the sharpest rise in cases in the last few weeks. B.1.1.7 — the more transmissible and more deadly variant of the coronavirus that was first discovered in Britain — may now make up around 70 percent of all of the state’s new cases, according to the Helix data.

Higher vaccination rates among the country’s older adults — those prioritized first in the vaccination rollout — mean that some of those at highest risk of complications are protected as cases rise again.

But almost 70 percent of the U.S. population has still not received a first dose, and only about half of those ages 65 and older are fully vaccinated. And in many states, those with high-risk conditions or in their 50s and 60s had not yet or had only just become eligible for the vaccine when cases began to rise again, leaving them vulnerable.

The tiny German state of Saarland, home to around 990,000 people, is making a cautious return to a new kind of normal in a pilot project that state officials hope could show how to keep the local economy open while controlling infections. From Tuesday, residents who test negative for the coronavirus will be able to use outdoor dining areas, gyms and movie theaters and even attend live theater performances.

Even as cases have continued to rise in Germany, prompting calls for a harsher national lockdown to halt a third wave of the pandemic — which has already shut down many of its European neighbors.

“More vaccinating, more testing, more mindfulness, more options: That’s the formula we want to use as Saarland break new ground in the fight against the coronavirus pandemic,” Tobias Hans, the governor of the state in southwestern Germany, said last week as he announced the reopening plans.

Under the guidelines, as many as 10 people can meet outdoors, and anyone with a negative test result within the previous 24 hours can visit stores, gyms, theaters and beer gardens — places that have largely been closed across Germany since the country announced a “lockdown light” in November.

(Many stores have been open since March, when a court overturned the rules.)

The Saarland project begins the same day that new regulations require travelers from the Netherlands to present a negative coronavirus test to cross the border into Germany. Travelers from the Czech Republic, France and Poland face similar measures.