WILMINGTON, Del. — Joseph R. Biden Jr. and his newly selected running mate, Senator Kamala Harris of California, called on Thursday for Americans to be required to wear masks, offering one of the first glimpses at how the Democratic ticket plans to confront the coronavirus and draw a contrast with President Trump.

Mr. Biden, addressing reporters after receiving a briefing from public health experts, said every American should wear a mask while outside for at least the next three months and that all governors should mandate mask wearing.

“It’s not about your rights,” Mr. Biden said, standing in front of five American flags at the Hotel du Pont in Wilmington. “It’s about your responsibilities as an American.”

Ms. Harris, appearing jointly with Mr. Biden for a second consecutive day, presented his call for mask-wearing as an example of what he would bring to the presidency — providing an early example of how she may try to talk up Mr. Biden to the American people.

“That’s what real leadership looks like,” she said. “We just witnessed real leadership.”

For months, Mr. Biden has assailed Mr. Trump over his handling of the pandemic, and the issue is likely to remain a central argument for Mr. Biden and now Ms. Harris in the final months of the campaign. The mask issue is an area that allows for a clear distinction with how Mr. Trump has approached the virus and how he has used — or not used — the platform that comes with the presidency to set an example for the American people.

Mr. Trump, who has ignored or mischaracterized scientific data throughout the pandemic, opened a White House press briefing on Thursday by calling Mr. Biden’s views “anti-scientific.”

Mr. Trump suggested that a mask mandate threatened to overstep individual freedoms of Americans and said Mr. Biden was more interested in keeping Americans “in their basements for months on end” than in listening to medical experts.

“If the president has the unilateral power to order every single citizen to cover their face in nearly all instances, what other powers does he have?” Mr. Trump said.

Mr. Biden, the former vice president, had previously said that as president, he would seek to require people to wear masks in public. Mr. Trump, on the other hand, resisted wearing a mask before shifting on the issue.

The virus continues to loom over Mr. Trump as a major political liability. Fifty-seven percent of Americans said the president was doing a bad job dealing with the virus, and 52 percent said the United States’ response was worse than other countries’, according to a Monmouth University poll released Thursday.

And in Wisconsin, an important battleground state, 69 percent of voters said people should be required to wear masks in all public places, according to a poll released Tuesday by Marquette University Law School. Polling by Quinnipiac University last month found that four in five voters in Florida and Texas also supported mask mandates.

In addition to the briefing on the virus on Thursday, Mr. Biden and Ms. Harris also received a briefing on the economic situation, with experts appearing by videoconference in both sessions. Janet L. Yellen, the former Federal Reserve chair, was among the participants in the economic briefing, the Biden campaign said.

As for their own mask etiquette, Mr. Biden and Ms. Harris did not wear masks, but were seated at a distance, when reporters were briefly allowed into the meeting on the virus. When they later addressed reporters, they wore masks until they got to the lectern, and then put their masks back on after they finished speaking.

Ms. Harris tried to cast doubt on the Trump administration’s efforts to develop a vaccine in a speedy manner, suggesting that what mattered was when that vaccine would be available to the public.

“I think it’s important that the American people, looking at the election coming up, ask the current occupant of the White House: When am I going to get vaccinated?” Ms. Harris said. “Because there may be some grand gestures offered by the current president about a vaccine. But it really doesn’t matter until you can answer the question: When am I going to get vaccinated?”

As Mr. Biden and Ms. Harris put their focus on the pandemic, Mr. Trump continued to ridicule Ms. Harris in a television interview, auditioning one of his demeaning schoolyard nicknames — a go-to Trump tactic that some Republican officials worry will backfire among suburban women who will see such an attack as sexist.

“Now you have sort of a mad woman, I call her, because she was so angry and such hatred with Justice Kavanaugh,” he told Maria Bartiromo, an ally who hosts a morning show on the Fox Business Network. “I mean, I’ve never seen anything like it. She was the angriest of the group, and they were all angry. They’re all radical-left angry people.”

But Mr. Trump’s attacks on Ms. Harris seem to have had little initial impact so far; one person close to Mr. Trump deplored what he saw as positive media coverage of the Biden-Harris announcement but conceded it had been “a nearly perfect rollout.”

Republican officials say that their focus groups on Ms. Harris show she is vulnerable to carefully framed criticism that avoids divisive political attacks on gender and race, instead portraying her as an out-of-touch coastal elitist who has little in common with working-class women. The officials spoke on condition of anonymity because they were not authorized to speak for the Trump campaign.

Mr. Trump, however, demonstrated on Thursday that he is unable to follow a surgical approach. At the White House briefing, he encouraged a racist conspiracy theory that is rampant among some of his followers: that Ms. Harris is not eligible for the vice presidency or the presidency because her parents were immigrants.

That assertion is false; Ms. Harris was born in California and is eligible to serve.

Mr. Trump also said in an interview on Thursday that he planned to deliver his renomination speech at the Republican National Convention from the South Lawn at the White House, a move that raises legal questions about using federal property for campaign purposes.

The day’s events came at a moment of muted optimism for a president whose approval numbers have tanked in recent months.

Internal campaign and party polling shows Mr. Trump recovering significant ground in several states, including Florida, which several of his aides attributed to his increased focus on the pandemic. (Recent public polling shows Mr. Biden maintaining a small lead in Florida.)

Nobody in Mr. Trump’s circle wants him to stop attacking. But some now fear some of those gains will evaporate if he attacks Ms. Harris with the same caustic abandon that characterized his attacks on Mrs. Clinton four years ago.

Republicans have also had difficulty in executing a coherent strategy against Mr. Biden. They have hit him with a buckshot spray of criticism — calling him soft on China, casting him as too tough on crime for party progressives, and, at the same time, labeling him as anti-police over his embracing of peaceful protests in the wake of the George Floyd killing.

Vice President Mike Pence, visiting Iowa on Thursday, sought to paint both Mr. Biden and Ms. Harris as anti-police and to stoke fears over public safety.

“The truth is you won’t be safe in Joe Biden’s America,” Mr. Pence said at a town hall discussion on law enforcement put on by Heritage Action for America, a conservative group.

Mr. Biden has supported redirecting some funding from the police but has rejected the “defund the police” movement. Ms. Harris, before she was Mr. Biden’s running mate, spoke about “reimagining” the role of law enforcement in America.

Thomas Kaplan reported from Wilmington, and Glenn Thrush from Washington. Michael Gold and Shane Goldmacher contributed reporting from New York, and Katie Rogers from Washington.