President Biden said on Tuesday that the United States was “on track” to have enough supply of coronavirus vaccines “for every adult in America by the end of May,” accelerating his effort to deliver the nation from the worst public health crisis in a century.

In a brief speech at the White House, Mr. Biden said his administration had provided support to Johnson & Johnson that would enable the company and its partners to make vaccines around the clock. The administration had also brokered a deal in which the pharmaceutical giant Merck would help manufacture the new Johnson & Johnson coronavirus vaccine.

Merck is the world’s second-largest vaccine manufacturer, though its own attempt at a coronavirus vaccine was unsuccessful. Officials described the partnership between the two competitors as historic and said it harked back to Mr. Biden’s vision of a wartime effort to fight the coronavirus, similar to the manufacturing campaigns when Franklin D. Roosevelt was president.

Originally, Johnson & Johnson’s $1 billion contract, negotiated last year when Donald J. Trump was president, called for the company to deliver enough doses for 87 million Americans by the end of May. Added to pledges from Moderna and Pfizer-BioNTech to deliver enough doses to cover a total of 200 million Americans by that date, the contract would have given the country enough vaccine for all adults 18 and older.

But Johnson & Johnson and its partners fell behind in their manufacturing. Although the company was supposed to deliver its first 37 million doses by the end of March, it said that it would be able to deliver only 20 million doses by that date, which made Biden aides nervous.

In late January, Jeffrey D. Zients, Mr. Biden’s coronavirus response coordinator, and Dr. David Kessler, who is managing vaccine distribution for the White House, reached out to top officials at the company, including Alex Gorsky, its chief executive, with a blunt message: This is unacceptable.

That led to a series of negotiations in February in which administration officials repeatedly pressured Johnson & Johnson to accept that they needed help, while urging Merck to be part of the solution, according to two administration officials who participated in the discussions.

In a statement on Tuesday, Merck said that the federal government would pay it up to $269 million to adapt and make available its existing facilities to produce coronavirus vaccines.

One federal official, who spoke on the condition of anonymity, said other steps that the administration took would move up Johnson & Johnson’s manufacturing timeline.

Those steps, said Jen Psaki, the White House press secretary, included providing a team of experts to monitor manufacturing and logistical support from the Defense Department. In addition, the president will invoke the Defense Production Act, a Korean War-era law, to give Johnson & Johnson access to supplies necessary to make and package vaccines.

“This is a type of collaboration between companies we saw in World War II,” Mr. Biden said at the White House. He thanked Merck and Johnson & Johnson for “stepping up and being good corporate citizens during this crisis.”

Noah Weiland contributed reporting.