WASHINGTON — 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 & Co. 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 harks 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.

“As a consequence of the stepped-up process that I’ve ordered and just outlined, this country will have enough vaccine supply — I’ll say it again — for every adult in America by the end of May,” Mr. Biden said. “By the end of May. That’s progress — important progress.”