WILMINGTON, Del. — President-elect Joseph R. Biden Jr. on Monday sharpened his criticism of President Trump’s refusal to cooperate in an orderly transition, warning that “more people may die” from the coronavirus if the president does not agree to coordinate planning for the mass distribution of a vaccine when it becomes available.

It was a marked shift in tone for the president-elect, intended to pressure Mr. Trump after Mr. Biden and his team had played down the difficulty of setting up a new government without the departing administration’s help. The new criticism came as the White House national security adviser all but conceded that Mr. Biden would be inaugurated and acknowledged the importance of a smooth federal handoff.

“The vaccine is important. But it’s of no use until you’re vaccinated,” Mr. Biden said, pledging to work with Republicans to defeat the virus and spur an economic revival when he takes office. But he said the logistics of distributing vaccines to hundreds of millions of Americans were a vast challenge. “It’s a huge, huge, huge undertaking,” he said.

“If we have to wait until Jan. 20 to start that planning, it puts us behind,” Mr. Biden said. “More people may die if we don’t coordinate.”

Over the weekend, the president again refused to acknowledge Mr. Biden’s victory and on Monday morning tweeted, “I won the Election!” Without a concession from Mr. Trump, the official transition remains frozen — and could stay that way for months.

Mr. Biden made his comments at a news conference after he and Vice President-elect Kamala Harris had discussed reviving the economy at a virtual meeting with business and labor leaders, including Mary Barra, the chief executive of General Motors, and Satya Nadella, the head of Microsoft, as well as the A.F.L.-C.I.O. president, Richard Trumka, and the United Auto Workers president, Rory Gamble.

“We all agreed that we want to get the economy back on track and get our workers back in the job by getting the virus under control,” Mr. Biden said. “We are going into a very dark winter. Things are going to get much tougher before they get easier. And that requires sparing no effort to fight Covid.”

Mr. Biden reaffirmed his support for a $3.4 trillion stimulus bill that House Democrats passed this year that Senate Republicans have rejected, though he offered no hint of a compromise that could break Congress’s monthslong deadlock.

But to do that, he said, will require new cooperation from Republicans, even those who have so far refused to publicly acknowledge Mr. Biden’s victory. Asked what he would say to members of the president’s party who have backed Mr. Trump’s refusal to concede, Mr. Biden said he would offer them an open hand.

“My message is: ‘I will work with you. I understand a lot of your reluctance because of the way the president operates,’” Mr. Biden said, adding that such conversations may not take place until Mr. Trump and his advisers have left office. “That’s a shame, but maybe that’s the only way to get it done.”

Mr. Biden praised the Republican governors of North Dakota, Ohio and Utah, who have each taken steps to lock down their states in response to the virus — and drawn attacks from Mr. Trump in the process. Monday morning, the president hinted in a tweet that he might support a primary challenge to one of them — Gov. Mike DeWine of Ohio.

“Who will be running for Governor of the Great State of Ohio? Will be hotly contested!” Mr. Trump wrote.

Mr. Biden said during his remarks that he had “enormous respect” for the Republican governors, including Mr. DeWine, who have bucked a president of their own party to insist that people wear masks.

“It’s about being patriotic. It’s about saving lives for real. This is not hyperbole,” Mr. Biden said, adding, “There is nothing macho about not wearing a mask.”

By contrast, Mr. Biden was sharply critical of administration officials including Dr. Scott Atlas, the radiologist who has emerged as the president’s most trusted adviser on combating the virus. Dr. Atlas has mocked the idea of wearing masks and recently urged people to “rise up” in protest of tough new restrictions in Michigan and elsewhere that were put in place to slow the spread of the virus.

The president-elect said Dr. Atlas’s call for people to resist the restrictions went against the recommendations of health professionals across the country. “What are they doing?” Mr. Biden said. “It’s totally irresponsible.”

Mr. Biden also said that he would “set an example” for Americans who may be wary of getting vaccinated, saying that if promising vaccines continue to prove safe and effective, “I would take the vaccine.”

Mr. Biden blamed Mr. Trump for anxiety among some Americans about the safety of the vaccine. Polling has shown concern that Mr. Trump’s enthusiastic claims about the pace at which vaccines have progressed under his administration’s Operation Warp Speed initiative could reflect unsafe politicization of the scientific process.

“Look, the only reason people question the vaccine now is because of Donald Trump,” Mr. Biden said. “That’s the reason why people are questioning the vaccine, because of all the things he says and doesn’t say — is it truthful or not truthful, the exaggerations.”

Mr. Biden urged Americans to limit any Thanksgiving gatherings to groups of no more than 10 people, socially distanced and wearing masks, and after quarantining. He said his own family plans were uncertain.

But on the larger question of Mr. Trump’s claims to victory, Mr. Biden was almost dismissive.

“I find this more embarrassing for the country than debilitating for my ability to get started,” Mr. Biden said. Of Mr. Trump’s weekend tweeting, he added: “I interpret that as Trumpism. No change in his modus operandi.”

A spokesman for Mr. Trump called Mr. Biden’s comments about endangered lives from a delayed transition “irresponsible and not based on fact,” insisting that the Centers for Disease Control and Prevention has made its plan for distributing the virus publicly available.

The spokesman, Judd Deere, said the administration was prepared “to ship vaccine doses to every ZIP code in America” within 24 hours of approval by the Food and Drug Administration.

Mr. Biden’s comments came as governors across the country have begun issuing tough new restrictions on businesses, schools, bars and sports venues in an effort to slow the spread of the virus, prompting an increasingly aggressive backlash from Republicans, including some of Mr. Trump’s advisers.

In Michigan, Gov. Gretchen Whitmer’s decision to shut down casinos, movie theaters and indoor dining — and to halt in-person learning at high schools and colleges — for three weeks prompted Republican lawmakers to call for her impeachment. She said the remarks by Dr. Atlas were “irresponsible” and left her breathless.

Hours before Mr. Biden’s remarks, Mr. Trump’s national security adviser, Robert C. O’Brien, went further than any other senior Trump official in a public forum when he said that Mr. Biden appeared to have won the election and pledged a smooth transition from his staff.

“Look, if the Biden-Harris ticket is determined to be the winner — and obviously things look that way now — we’ll have a very professional transition from the National Security Council,” Mr. O’Brien said.

Perhaps wary of the ire of a president who refuses to concede the obvious, however, even Mr. O’Brien spoke conditionally, falsely suggesting that the elections’s outcome remains uncertain.

“If there is a new administration, they deserve some time to come in and implement their policies,” Mr. O’Brien said during a talk recorded last week and streamed on Monday as part of a conference hosted by the Center for Strategic and International Studies.

“And if we are in a situation where we are not going into a Trump second term, which I think people where I’m sitting in the White House would like to see, if it’s another outcome, it will be a professional transition — there’s no question about it,” he added.

Jim Tankersley and Alan Rappeport contributed reporting.

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