The AstraZeneca Covid-19 vaccine has been authorized for use in more than 70 countries, but the United States is not yet one of them. And as American officials wait for results from the company’s U.S. trial and then emergency clearance, tens of millions of doses sit idly in American manufacturing facilities — even as other countries beg for access.

The doses’ fate is the subject of an intense debate among White House and federal health officials. Some argue that the administration should let them go abroad where they are desperately needed, while others are not ready to relinquish them.

AstraZeneca, a British-Swedish company, is involved in those conversations.

In a prime-time speech to the nation on Thursday, President Biden said the government had made major gains in securing vaccines for the United States. By the end of May, he said, there will be enough for all adults in the country, and promised that by May 1 every adult will be eligible for one.

But other countries are grappling with serious supply issues, and a shortfall in the supply of the AstraZeneca vaccine has fueled tensions with European officials.

AstraZeneca has asked the Biden administration to let it send the American doses to the European Union. The administration, for now, has denied the request, one official said.

The company’s Covid-19 vaccine has meanwhile hit some headwinds this week after health authorities in three European countries suspended its use as a precaution while European drug regulators investigate the possibility that it might increase the risk of blood clots. The countries — Denmark, Iceland and Norway — emphasized that there was no evidence of any causal link. Bulgaria and Thailand suspended use of the vaccine on Friday.

Denmark acted after a 60-year-old woman who received a shot developed a blood clot and died. Several other European countries had stopped using doses from the same vaccine batch after some reports of severe blood clots, and European drug regulators are investigating.

Public health experts expect medical conditions to turn up by chance in some people after receiving any vaccine. In the vast majority of cases, such illnesses have nothing to do with the shots. Most other countries where the AstraZeneca vaccine has been given to many millions of people have not reported similar red flags.

The Biden administration’s hesitation in letting go of the vaccine doses is at least partly related to uncertainties with supply before a benchmark of late May laid down by the president. Vaccine production is notoriously complex and delicate, and problems like mold growth can interrupt a plant’s progress.

The administration’s moves to order more supply of the three vaccines authorized by the F.D.A. has further sidelined AstraZeneca’s candidate. The United States may only briefly, or never, need the AstraZeneca doses.

Hungary has agreed to pay about $36 a dose for the Covid-19 vaccine made by Sinopharm, a Chinese state-owned company, according to contracts made public by a senior Hungarian official on Thursday. That appears to make the Sinopharm shot among the most expensive in the world.

Hungary has agreed to buy five million doses of the Sinopharm vaccine, priced at 30 euros ($36) each, according to contracts that Prime Minister Viktor Orban’s chief of staff, Gergely Gulyas, uploaded to his Facebook page. The contract is between the Hungarian government and a third-party vendor, and that price far surpasses what the European Union has agreed to pay for vaccines from Western manufacturers.

The European Union has said it would pay €15.50 per dose for the Pfizer-BioNTech vaccine, according to Reuters, which cited an internal E.U. document. For AstraZeneca, it agreed to pay $2.15 per dose, according to Belgium’s budget secretary.

The contracts that Mr. Gulyas published also show that Hungary, which has recorded nearly half a million coronavirus cases and more than 16,000 deaths, has agreed to pay $9.95 per dose for the Russian Sputnik-V vaccine.

The company from which Hungary is buying the vaccine underwent a change in ownership two months before the transaction, was awarded the contract after the government exempted it from having to take part in an open public procurement process, said Miklos Ligeti, legal director for Transparency International Hungary, an anticorruption group. (Because of an editing error, an earlier version of this article misstated which company had changed ownership.)

Such arrangements raise red flags for anticorruption watchdogs, who warn that the involvement of third parties increases the risk of price gouging. “We don’t know how much this company actually paid for this vaccine,” Mr. Ligeti said.

Given publicly available data on this company, Mr. Ligeti pointed to figures that he described as worrying. “The government of Hungary assigned a contract with a net value of 150 million euros” — $179 million — “to a company with registered capital of €9,000” ($10,700), he said.

Hungary is one of the few European countries to sign a deal with Sinopharm, which has promoted itself to developing countries at a time when many richer nations are hoarding doses by Western drugmakers like Pfizer and Moderna. A major selling point has been Sinopharm’s manufacturing capacity: It has said it can make up to three billion doses by the end of this year.

The Sinopharm price is extraordinary in part because the company, unlike the Western vaccine makers, has not published detailed data from Phase 3 trials.

Sinopharm is mass-producing two vaccines. It says that the first, made in conjunction with the Beijing Institute of Biological Products, has an efficacy rate of 79 percent, and that the second, made with the Wuhan Institute of Biological Products, is 72.5 percent effective.

Adam Liptak contributed reporting.

Four former U.S. presidents and their first ladies appear in a new public service campaign with one single plea to Americans: Get vaccinated.

The ads feature former Presidents Jimmy Carter, Bill Clinton, George W. Bush and Barack Obama, getting vaccine jabs. Their wives — Rosalynn Carter, Hillary Clinton, Laura Bush and Michelle Obama — also appear.

The two ads urge all Americans to get their shots when the opportunity arrives.

“This vaccine means hope,” Mr. Obama says. “It will protect you and those you love from this dangerous and deadly disease.”

“In order to get rid of this pandemic it’s important for our fellow citizens to get vaccinated,” says Mr. Bush.

They spoke of the longing so many feel to get back to normal.

“I want to be able to go back to work and to move around,” says Mr. Clinton.

“To visit with Michelle’s mom,” says Mr. Obama. “To hug her, and see her on her birthday.”

Mr. Bush says he is “really looking forward to going to opening day in Texas Ranger Stadium with a full stadium.”

Mr. Carter says, “I’m getting vaccinated because we want this pandemic to end as soon as possible.”

The only ex-presidential couple not in the ad campaign is Donald and Melania Trump.

Mr. and Mrs. Trump quietly received their vaccines in January before leaving the White House. Later that month, Mr. Trump appeared at the CPAC political conference in Orlando, Fla., where he encouraged people to go get vaccinated.

Mr. Trump’s private approach came as a number of his supporters have expressed resistance to the vaccine. Many other prominent figures have tried setting an example by getting the shot in public. Last week, Andy Slavitt, a senior White House pandemic adviser, dodged a question from a reporter about whether the Biden White House would ask Mr. Trump to do a public service announcement to encourage hesitant supporters to get vaccinated. Mr. Slavitt said that many people, including Republican politicians, have spoken up about the importance of getting vaccinated.

“I particularly liked the Dolly Parton song myself,” Mr. Slavitt said, referring to the country music star breaking into song when she received her first dose of the vaccine. “That’s one of my favorites.”

The two ads are part of a broad promotional effort to combat Covid-19 vaccine skepticism that launched in February, backed by the nonprofit adverting group Ad Council and a coalition of experts known as the Covid Collaborative. Public service announcements will appear in English and Spanish on television, social media and other platforms.

More than 300 companies, community groups and public figures contributed to the $52 million push, as did the Centers for Disease Control and Prevention.

“We urge you to get vaccinated when it’s available to you,” says Mr. Obama.

“So roll up your sleeve and do your part,” says Mr. Bush.

“This is our shot,” says Mr. Clinton.

“Now it’s up to you,” concludes Mr. Carter.

Eileen Sullivan contributed reporting.

China imposed some of the world’s toughest lockdowns to stop the coronavirus. One city sealed apartment doors, leaving residents with dwindling food and medicine. One village tied a local man to a tree after he left home to buy cigarettes.

Few officials spoke up against the measures, given the central government’s obsession with its anti-coronavirus campaign. That hasn’t stopped Dr. Zhang Wenhong.

Dr. Zhang, an infectious-disease specialist and perhaps China’s most trusted voice on Covid-19, has spoken out publicly against the strictest lockdowns. Fighting the pandemic, he likes to say, is like “catching mice in a china shop.”

He may be China’s closest analogue to Dr. Anthony S. Fauci, the American infectious-disease specialist who became the public face of the response to the virus in the United States.

A consummate technocrat, Dr. Zhang comes across as neither political nor ideological. Yet by offering his expert opinions straight, he pushes back against the authoritarian instinct in a system that often turns to draconian measures.

A top academic at Fudan University in Shanghai and a member of the Communist Party, Dr. Zhang led Shanghai’s expert panel on Covid-19, giving him considerable authority over the city’s response.

But unlike Dr. Fauci, who urged the Trump administration to do more, Dr. Zhang championed a more strategic approach for a country that didn’t take coronavirus half-measures. In doing so, he spoke to the Chinese public with respect, a refreshing change from the way others in authority often carry themselves.

Dr. Zhang is especially popular among professionals and technocrats who admire him for his sincerity in a society plagued by propaganda, conspiracy theories and crude nationalism.

“At this moment, rumors are more terrifying than the virus,” he said at the beginning of the outbreak. “We need to explain the epidemic to the public with rational data and professional knowledge.”

In today’s China, getting ahead often means speaking in the language of the Communist Party. Those who refuse to ride the ideological tide keep their independence by keeping quiet.

By contrast, Dr. Zhang has earned an ability to speak freely. Shanghai, a city of 24 million people, has had only 371 local infections and seven deaths.

His forecasts have been on the mark. He predicted early on that the pandemic could last at least one to two years. A year ago this month, when China was still virtually shut down, he said China had left its toughest hours behind.

Journalists began to seek him out, and some of his responses became internet memes. A few examples:

“Influenza is not a cold, just like a tiger is not a cat.”

“You’re bored to death at home, so the virus will be bored to death, too.”

The drug company Novavax said on Thursday that its coronavirus vaccine candidate had an efficacy rate of 96.4 percent in a Phase 3 trial in Britain, a clinical result on par with that of the Moderna and Pfizer-BioNTech shots.

But the Novavax candidate was only 48.6 percent effective in a Phase 2 trial in South Africa, where most cases are linked to an emerging variant, the company said.

The 96.4 percent rate measured the drug’s efficacy in Britain against mild, moderate and severe disease caused by the “original” strain of the coronavirus, Novavax said in a statement. The rate declined to 86.3 percent in cases caused by the B.1.1.7 coronavirus variant, which was first detected in Britain.

The 48.6 percent rate in the South Africa trial applied to “predominantly variant strains” of the virus, Novavax said, although it noted that the vaccine still offered 100 percent protection against severe disease and death in both trials.

Most of the cases circulating in South Africa are linked to the B.1.351 variant. Scientists are concerned, because clinical trials tend to show that vaccines offer less protection against it than other variants.

The findings released on Thursday are not a huge departure from interim results, released by Novavax in January, that showed an efficacy rate of nearly 90 percent in Britain and just under 50 percent in South Africa.

Novavax, a little-known company based in Maryland, has never brought a vaccine to market. It is working on one of six vaccine candidates supported by the U.S. government’s Operation Warp Speed and has been running trials in Britain, Mexico, South Africa and the United States.

The company said in January that it had started working on a new version of the vaccine to address the more contagious variants.

Global roundup

NEW DELHI — India has recorded one of its worst single-day increases in coronavirus cases since late December, owing largely to a resurgence in the western state of Maharashtra. More than 60 percent of the country’s 23,285 cases on Thursday were reported from the state, according to data from the health ministry.

This month the government of Maharashtra, where the country’s financial capital, Mumbai, is located, imposed a lockdown in some areas after cases surged to over 8,000 in a single day. On Friday, officials announced fresh restrictions in other parts of the state.

A strict lockdown was imposed for a week in the city of Nagpur beginning on Monday, the central and state governments said.

Until last month, India had been experiencing somewhat of a breather in its outbreak. During the peak of its outbreak last fall, the country was registering more than 90,000 cases a day, but cases fell rapidly over the next few months to just about 9,000 a day, according to a New York Times database.

“We are very worried about Maharashtra,” Vinod K. Paul, one of the country’s top health officials, said at a news conference on Thursday. “In all the states where the virus is seemingly on the rise in a significant way, the vaccination eligibility in those areas should be intensified,” he said.

As of Friday morning, India had vaccinated 26 million people against the coronavirus. The government has set a target of 300 million inoculations by July.

In other news from around the world:

• The health authorities in Germany will remove parts of Spain and Portugal from a list of high-risk areas that the government warns against — but doesn’t forbid — traveling to starting on Sunday. Among the delisted areas in Spain are the Balearic Islands, which include Mallorca, a popular destination for German tourists. Others being taken off the list: the central areas of Castilla-La Mancha, Extremadura, La Rioja, Murcia and Valencia, in addition to the Portuguese regions Alentejo and the Azores. Although travelers coming from Germany no longer have to quarantine before hitting the beaches, they will have to show a negative virus test before departing Germany, which Spain considers a high-risk area.

• Prime Minister Chung Sye-kyun of South Korea said on Friday that coronavirus restrictions would remain in effect until March 28, the Yonhap news agency reported. The rules, which vary by region but include a nationwide ban on most private gatherings, was set to expire on Sunday. South Korea reported 488 cases on Friday, a three-week high. The government has said it aims to achieve herd immunity by November, but only about 1 percent of the country’s 51 million people have been vaccinated.

• After months in lockdown, Wales will ease its restrictions starting Saturday, the country’s leader announced. The nation’s stay-at-home order will be replaced by guidance to stay local, and the new rules will permit up to four people from two households to meet together outdoors, and outdoor sport and visits to care homes to restart. “The journey out of lockdown begins in earnest in Wales this weekend,” First Minister Mark Drakeford said on Friday. The gradual approach to reopening will allow haircut appointments from Monday, and shops will be able to welcome customers back on April 12, the same date as they are set to reopen in England.

Anna Schaverien and Christopher F. Schuetze contributed reporting.

Countries continued to shy away from using the AstraZeneca vaccine on Friday, a day after Demark, Norway and Iceland said they would halt its use while European drug regulators examine the possibility of a link to blood-clotting issues. The moves come despite continued support for the vaccine from global health authorities.

Bulgaria joined those countries on Friday, saying it would temporarily suspend inoculations with the AstraZeneca vaccine after the death of a woman a day after she received a shot. And Thailand delayed its rollout of the vaccine, which was to begin Friday.

Both countries said they were acting out of an abundance of caution, and Bulgaria said an autopsy of the woman did not find any traces of blood clots.

Margaret Harris, a W.H.O. spokeswoman, said at a briefing on Friday that AstraZeneca was an “excellent vaccine,” Reuters reported, and that no causal relationship had been shown between the vaccine and reports of blood coagulation. Health officials worry the suspensions will cause more hesitancy about taking vaccines, a crucial tool in combating the pandemic.

Italy and Romania also paused shots on Thursday, but only from a single batch of the vaccine that Italy is investigating. That batch is different from the one that set off alarms in Denmark and several other countries starting last weekend.

Bulgaria — which is experiencing a third wave of the virus — ordered the temporary suspension on Friday after the death of the woman, who was 57, the country’s health minister, Kostadin Angelov, told reporters. There is no indication that the death is related to the vaccination, but the health authorities are investigating.

Mr. Angelov said the woman had several pre-existing conditions, including a history of heart disease.

“I do not expect to find any correlation even in this case” between the death and vaccine, Mr. Angelov said. “However, having the people’s health and well-being in mind, we decided to take action as a precaution.”

The move could further hinder Bulgaria’s efforts in a vaccination campaign that has been marred by a slow rollout and vaccine hesitancy. The country relies heavily on the AstraZeneca vaccine, and has ordered 4.5 million doses.

In an effort to speed up its inoculation campaign, Bulgaria introduced a walk-in vaccination program last month under which anyone wanting to be inoculated would receive an AstraZeneca shot. Since then, those “green corridors” have been switched on and off amid a shortage of doses.

Thailand’s announcement came hours before Prime Minister Prayuth Chan-ocha was scheduled to be the first person in the country to be inoculated with a shot of AstraZeneca, and the move does not affect Thailand’s rollout of the Sinovac vaccine.

Dr. Yong Poovorawan, a virologist at Chulalongkorn University in Thailand, told reporters that the country’s delay would probably last a week or two. “We’re not saying the vaccine is bad,” he said of the AstraZeneca vaccine. “We’re postponing it to see if the deaths are related to the vaccine or not.”

One year ago, New Yorkers were told to keep their hands away from their faces — and from people and banisters and elevator buttons. When the hands failed to obey, they were scrubbed to the bone.

For all of the uncertainty and terror that greeted the arrival of the coronavirus, there was a certain clarity to the early protocols.

Now, after so much tragedy, the city finds itself closer to the point of normalcy. By the end of this week, more than 2.4 million doses of the Covid vaccines will have been administered in New York City, which was once the global epicenter of the pandemic.

This period in the aftermath of lockdown and before a complete reversion to ordinary routines is rife with its own confusion and conflicts.

“It is clear from walking around the city that people are giving in and relaxing rules, probably because of progression in vaccinations and because people are experiencing extreme fatigue,” Emanuela Taioli, the director of Translational Epidemiology at Mount Sinai, told me.

“The reality is that the positivity rates in the city are not going down,” she said. “They are at a plateau and staying there. This has been true for the last two weeks. This means that we have to keep going with the precautions until we are all vaccinated, and that may take another couple of months or more.”

Who wants to hear this? Probably no one.

In Texas, where Gov. Greg Abbott recently lifted a mask mandate, a bar called Shenanigans and Confetti’s Beach Club, in the town of Huntsville, advertised a “Masks Off” party for this past Tuesday night with “100 percent capacity.’’

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On Tuesday, the journal Science reported that the United States, by contracting with multiple pharmaceutical companies out of precaution, had essentially over-ordered vaccine doses. This whiplash notion of scarcity and abundance has led many people to rationalize being vaccinated even if they don’t technically meet eligibility requirements.

It may seem morally reprehensible that a wealthy Brooklynite — claiming asthma or A.D.H.D. as a developmental disability, for example — will travel to a poorer neighborhood to get vaccinated. But epidemiologists turn out to be not in the castigation business when it comes to immunization. They say the point is to get as many people jabbed as possible.

How will we look at this precarious time a year from now? How will we regard the choices we make to jump-start regular life or to wait our turn to hit the piñata? It will depend on the outcome, the worst one being that the powerful go on living as always have, and the vulnerable become even more so.

Italy’s government said Friday that coronavirus restrictions would be severely tightened across much of the country starting Monday and that the entire country would be under lockdown over Easter weekend to beat back surging infections amid a slow vaccine rollout.

The office of Italy’s new prime minister, Mario Draghi, announced the measures, which will force more than half of Italy’s population into lockdown. Starting Monday, health authorities will shut down schools, restaurants and many shops in most northern regions as well as the regions of Rome and Naples. People will also be restricted from leaving their homes except for work, health care visits and emergencies.

For Easter weekend, April 3-5, which is usually celebrated with large family gatherings, a lockdown will limit movement to one trip a day out of the home.

The measures are among the strongest since last March, when Italy became the first Western country to impose a lockdown in an effort to slow the spread of the virus.

“I am aware that today’s measures will have an impact on children’s education, on the economy and also on the psychological state of us all,” Mr. Draghi said during a televised visit Friday to a vaccination hub near Rome. “But they are necessary to avoid a worsening that will make even more stringent measures inevitable.”

“The memory of what happened last spring is still vivid. We will do anything that we can to prevent it from happening again.”

Also Friday, Italy’s Health Ministry applied new criteria to determine when regions are shut down. The restrictions would take effect when the virus caseload surpasses 250 cases per 100,000 residents. Many of the country’s 20 regions are expected to be subjected to the measures.

Italy surpassed 100,000 coronavirus deaths this week, with a current death rate of about 300 per day. The country registered over 25,000 new infections and 373 deaths on Thursday.

Some health officials attribute the rise in contagions and death, especially in central and northern Italy, to the now widespread presence of a more contagious variant first reported in Britain. Italy’s vaccine rollout, as in other European countries, remains slow compared with the United States and Britain. About 7 percent of Italy’s population has been vaccinated.

The country has encountered delays in vaccine deliveries from Pfizer-BioNTech, Moderna and AstraZeneca. And the country’s own difficulties in managing vaccine distribution in the underdeveloped south and in the wealthy, hard-hit region of Lombardy have also slowed things down.