The United States plans to send millions of doses of the AstraZeneca vaccine to Mexico and Canada, the White House said Thursday, a notable step into vaccine diplomacy just as the Biden administration is quietly pressing Mexico to curb the stream of migrants coming to the border.

Jen Psaki, the White House press secretary, said the United States was planning to share 2.5 million doses of the vaccine with Mexico and 1.5 million with Canada, adding that it was “not finalized yet, but that is our aim.”

Tens of millions of doses of the vaccine have been sitting in American manufacturing sites. While their use has already been approved in dozens of countries, including Mexico and Canada, the vaccine has not yet been authorized by American regulators. Ms. Psaki said the shipments to Mexico and Canada would essentially be a loan, with the United States receiving doses of AstraZeneca, or other vaccines, in the future.

The announcement of the vaccine distribution came at a critical time in negotiations with Mexico. President Biden has moved quickly to dismantle some of former President Trump’s signature immigration policies, halting construction of a border wall, stopping the swift expulsion of children at the border and proposing a pathway to citizenship for millions of immigrants in the United States.

But he is clinging to a central element of Mr. Trump’s agenda: relying on Mexico to restrain a wave of people making their way to the United States.

Anticipating a surge of migrants and the most apprehensions by American agents at the border in two decades, Mr. Biden asked President Andrés Manuel López Obrador of Mexico in a video call this month whether more could be done to help solve the problem, according to Mexican officials and another person briefed on the conversation.

The two presidents also discussed the possibility of the United States sending Mexico some of its surplus vaccine supply, a senior Mexican official said. Mexico has publicly asked the Biden administration to send it doses of the AstraZeneca vaccine.

At a news briefing on Thursday, Ms. Psaki said that the discussions over vaccines and border security between the United States and Mexico were “unrelated” but also “overlapping.”

Asked by a reporter if the United States had “strings attached” to its offer to lend vaccines to Mexico, Ms. Psaki replied that there were “several diplomatic conversations — parallel conversations — many layers of conversations” at play in the discussions.

“There’s rarely just one issue you’re discussing with any country at one time,” Ms. Psaki said. “Certainly that’s not the case with Mexico. It’s not the case with any country around the world. And so I wouldn’t read into it more than our ability to provide — to lend — vaccine doses.”

Mexican officials also say the efforts to secure vaccines are separate from the negotiations over migration, and rejected the notion that a quid pro quo was involved.

“These are two separate issues,” Roberto Velasco, director general for the North America region at Mexico’s foreign ministry, said in a statement, referring to the engagement between the two countries on migration and vaccines.

But Mexican officials acknowledge that relations between the United States and Mexico, which has suffered one of the world’s deadliest coronavirus epidemics, would be buoyed by a shipment of doses south.

“We look for a more humane migratory system and enhanced cooperation against COVID-19, for the benefit of our two countries and the region,” Mr. Velasco added.

Several European countries suspended use of the AstraZeneca vaccine this week, a precaution because some people who had received the shot later developed blood clots and severe bleeding. But on Thursday, Europe’s drug regulator declared the vaccine safe. AstraZeneca has also said that a review of 17 million people who received the vaccine found they were less likely than others to develop dangerous clots.

A Biden administration official declined to comment further on the negotiations with Mexico, but noted that both countries shared a common goal of reducing migration by addressing its root causes, and said they were working closely to stem the flow of people streaming to the border.

The Biden administration is facing intense pressure, scrambling to find shelter space for a growing number of migrant children and teenagers held in American detention facilities along the border.

More than 4,500 of them were stuck in detention facilities as of Thursday, with the Biden administration working on putting them in a convention center in Dallas, a former camp for oil workers in Midland, Texas, and possibly a NASA site in California.

The administration has also identified nearly a dozen other sites, including Defense Department facilities, to potentially house the children and teenagers until they can be placed with a sponsor, according to a government document from March obtained by The New York Times. One of the sites — in Pecos, Texas — could hold 2,000 beds.

Mexico has agreed to increase its presence on its southern border with Guatemala to deter migration from Central America, one of the government officials said, and local Mexican officials say their country has recently stepped up efforts to stop migrants on the northern border with the United States as well.

But there are also signs that Mexico’s commitment to policing migration — a central demand of Mr. Trump, who wielded the threat of tariffs against all Mexican goods unless migration was curbed — may have flagged in the waning months of the Trump administration.

From October through December of last year, the number of Central Americans apprehended by Mexico declined, while detentions by American agents increased, according to Mexican government numbers and data compiled by The Washington Office on Latin America, a research organization that pushes for human rights.

“The likelihood of the outgoing Trump administration threatening tariffs again was low, so there was an incentive for Mexico to go back to its default state of low apprehensions,” said Adam Isacson, an expert on border security at The Washington Office on Latin America.

The Biden administration’s appeal to do more against migration has put Mexico in a difficult position. While Mr. Trump strong-armed Mexico into militarizing the border, some Mexican officials argue that his harsh policies may have at times helped lessen their load by deterring migrants from attempting to make the journey north.

Mr. Biden is less likely to resort to threats of tariffs to get his way, officials and analyst say. But now Mexico is being asked to hold the line against a surge of migrants — while the Biden administration is signaling that the United States is more welcoming to migrants.

“They get to look like the good guys and the Mexicans look like the bad guys,” said Cris Ramón, an immigration consultant based in Washington, D.C.

“All the positive humanitarian policies are being done by the Biden administration.” Mr. Ramón added, “and then the Mexicans are left with the dirty work.”

As for Canada, several of Prime Minister Justin Trudeau’s political opponents repeatedly pressed him to lobby the new Biden administration for the release of vaccines. Many Canadians have expressed dismay that the United States had not shared any supplies with Canada, where no coronavirus vaccines are manufactured.

Until Thursday, all of Canada’s vaccine supply had come from Europe or India, and Canada’s roll out has proceeded at a slow pace compared with the United States and many other countries.

“God bless America, they’re coming to our rescue,” Doug Ford, the premier of Ontario, Canada’s most populous province, told a news conference.

While the Biden administration has committed to helping a major vaccine manufacturer in India, the United States has fallen far behind China, India and Russia in the race to use vaccines as diplomatic tools.

Beijing is shipping vaccines to dozens of countries, including some in Africa and Latin America. Russia has supplied its vaccine to Hungary and Slovakia. Mr. Biden has also drawn criticism for not making it easier for poorer countries to gain access to generic versions of coronavirus vaccines and treatments.

With Mexico, the Biden administration has been urging the country to accept more families expelled by American authorities, and to increase enforcement at Mexico’s southern border with Guatemala, according to two Mexican officials and two others briefed on the discussions.

Mr. López Obrador is also trying to find a way to increase capacity to house migrants in shelters, which are bursting at the seams. In a Tuesday statement, the secretary for homeland security, Alejandro Mayorkas, said he was working with Mexico to do that.

“Shelters are at a near collapse,” said Enrique Valenzuela, a lead coordinator for the government of Chihuahua state’s migration efforts.

Local government officials in Ciudad Juárez and shelter operators say Mexico is dialing up operations to capture and deport migrants along the northern border. On a near daily basis, two of them said, Mexican authorities are stopping vans stuffed with families and pickup trucks carrying livestock — along with migrants crouching on the floor to avoid detection.

Part of the reason Mexico is willing to continue cracking down is that, despite being a country that has long sent people north, there is a lot of resentment toward Central American migrants.

“The level of negative attitudes that we have toward migrant flows has gone up, so there won’t be a political cost” for Mr. López Obrador, said Tonatiuh Guillén, who ran Mexico’s National Migration Institute in the first half of 2019. “But with Trump, we negotiated nothing — we gave them a lot and they didn’t give us anything back,” he added, arguing that the strategy should be different with Mr. Biden.

Despite the very public tensions with Mexico under Mr. Trump, Mr. López Obrador has been wary of the Biden administration, concerned that it might be more willing to interfere on domestic issues like labor rights or the environment.

Instead, several Mexican officials say, his government has pushed the United States to deter Central Americans from migrating by sending humanitarian aid to Honduras and Guatemala in the wake of two hurricanes that devastated those countries and, many experts believe, pushed even more people to migrate.

Mexican officials have also asked the United States to send more Hondurans and Guatemalans apprehended in the United States directly to their home countries, rather than releasing them to Mexico, making it even harder for them to try to cross the border again.

The need for vaccines in Mexico is clear. About 200,000 people have died in the country from the virus — the third highest death toll in the world — and it has been relatively slow to vaccinate its population. That poses a potential political risk for Mr. López Obrador, whose party is heading into crucial elections in June that will determine whether the president hangs onto control of the legislature.

“Mexico needs cooperation from the U.S. in getting its economy jump-started and getting vaccines to get out of the health crisis,” said Andrew Selee, president of the Migration Policy Institute in Washington. “So there’s room for the two countries to reach agreements based on aligned interests rather than overt threats.”

Michael D. Shear, Ian Austen, Noah Weiland, Sharon LaFraniere and Eileen Sullivan contributed reporting.