WILMINGTON, Del. — President-elect Joe Biden sought to project the authority of an incoming president Monday as he dealt with matters domestic and international, even as the defeated incumbent continued to balk at turning over the reins.

Biden began taking calls from foreign leaders, speaking Monday with Canadian Prime Minister Justin Trudeau. He also was weighing whom to appoint to top White House positions, with several of his longtime advisers expected to take senior roles. And he turned his attention to the coronavirus, dispatching a key aide to brief Senate Democrats this week and making a strong pitch to Americans of every ideology to follow public health recommendations.

Biden urged Americans to wear masks, at one point holding one up during a speech in Wilmington, and sought to depoliticize the act of putting one on.

“We can save tens of thousands of lives if everyone would just wear a mask for the next few months,” said Biden, who wore a mask routinely during the campaign and was mocked by President Trump for doing so. “Not Democrat or Republican lives, American lives.”

Speaking on the day when the number of U.S. coronavirus cases soared past 10 million — the daily count has hit more than 100,000 recently — Biden sought to impart urgency about adopting actions to curb the spread, even as he acknowledged that he had little power other than rhetoric to change behavior.

“The challenge before us right now is still immense and growing, and although we are not in office yet, I’m just laying out what we expect to do and hope can be done,” said Biden, speaking from the Queen, a Wilmington theater, with Vice President-elect Kamala D. Harris at his side.

The effort to bend the trajectory of the coronavirus pandemic, which has killed more than 238,000 Americans, was part of Biden’s attempt to push as hard as he can at the notion that he will inevitably become president on Jan. 20, regardless of Trump’s sentiments.

But so far his transition lacks the latitude usually given to an incoming president by a conceding defeated leader.

Trump has continued to insist that he won the election, despite trailing Biden 279 electoral votes to 214. Biden leads in two states that have not been formally projected — Arizona and Georgia — while Trump leads in two others, North Carolina and Alaska.

“What President-elect Biden has to do is act like a winner, because he won,” said presidential historian Douglas Brinkley, who noted that Biden’s victory in the popular vote and the expected win in the electoral college are by unusually large margins. Still, given Trump’s recalcitrance, Brinkley said, it behooves Biden to be visible.

“You don’t want to be in quarantine or hiding mode,” he said. “Every day you have to move forward with the transition without being distracted by Trump’s antics.”

The president’s team has taken legal action to invalidate some ballots and question counting in several states, and his allies and advisers continue to insist — without proof — that Democrats cheated to clear a path for Biden’s election. The political appointee heading the General Services Administration, Emily Murphy, has so far declined to sign off on paperwork that would allow the Biden team to kick-start its transition with access to government offices and money to finance its effort.

On Capitol Hill, meanwhile, the president’s allies were walking in lockstep behind him.

Senate Majority Leader Mitch McConnell (R-Ky.) said Monday afternoon that the president is “100 percent within his rights” to take legal action to try to overturn the results.

“This process will reach its resolution. Our system will resolve any recounts” or lawsuits, McConnell said in remarks on the Senate floor.

McConnell on Monday did not congratulate Biden. His remarks came shortly after he met with Attorney General William P. Barr. A Justice Department spokeswoman declined to comment on the meeting.

Biden’s team has welcomed support from Republican senators willing to break with Trump and bolster the legitimacy of the election via congratulatory statements.

Sen. Ben Sasse (R-Neb.) congratulated Biden on Monday, calling him the “next president.”

A more nuanced statement came from Sen. Susan Collins (R-Maine), who last week won a fifth term. She congratulated Biden on his “apparent victory” but also said Trump should be “afforded the opportunity” to challenge the election’s outcome.

Collins, who is known to have a good relationship with Biden after they served in the Senate together for years, spoke with the Democrat last week, according to a Republican aide, who was not authorized to discuss private conversations and so spoke on the condition of anonymity.

More than 30 Republican former members of Congress released a statement calling on the nation to accept the outcome of the presidential election and denouncing Trump’s allegations of widespread fraud.

Senate Minority Leader Charles E. Schumer (D-N.Y.) urged GOP lawmakers to follow the lead of former president George W. Bush, who congratulated Biden in a statement Sunday.

“There has been no evidence of any significant or widespread voter fraud,” Schumer said. “Joe Biden won this election fair and square.”

Biden’s biggest task Monday was to grapple with the spiraling spread of the coronavirus. He named 13 top physicians and public health experts to a coronavirus advisory committee as his first official act as president-elect, a move meant to demonstrate his commitment to a science-based approach to containing the outbreak.

“This group will advise on detailed plans, built on a bedrock of science, and then keep compassion, empathy and care for every American at its core,” Biden said Monday, adding that the members will look at ways to increase access to rapid testing, determine how to hire a “corps” of contact tracers and prioritize how to get vaccines to the most at-risk Americans.

Physician Vivek H. Murthy, a co-chair of Biden’s coronavirus advisory board, was invited by Schumer to brief Senate Democrats at their caucus lunch Tuesday, according to a senior Democratic aide. The briefing will be held via phone, like all other Democratic lunches have been recently.

Despite Monday’s news that Pfizer’s vaccine has proved to be more than 90 percent effective at protecting people compared with a placebo — a mark higher than many experts had predicted — Biden sought to lower expectations about how quickly it could be approved and distributed, a departure from Trump’s insistence that a vaccine would be widely available soon.

“The expectation is the FDA will run a process of rigorous reviews and approval,” said Biden. “The process must also be grounded in science and fully transparent so the American people can have every confidence that any approved vaccine is safe and effective.”

He added another note of caution, saying, “It’s clear that this vaccine, even if approved, will not be widely available for many months yet to come.”

Biden’s conversation Monday with Trudeau was the first time he had been known to talk to a foreign leader since he claimed victory Saturday.

“We’ve worked with each other before, and we’re ready to pick up on that work and tackle the challenges and opportunities facing our two countries — including climate change and COVID-19,” Trudeau said in a message posted on social media. “. . . President-elect @JoeBiden and I agreed to keep in touch and work closely together.”

Topics included trade, energy, the NATO alliance and racial justice, Trudeau said.

Behind the scenes, Biden was also working to finalize his senior White House team.

Biden has previously blown past deadlines on important matters; he extended his decision on whether to run for president beyond his initial deadline and similarly took extra weeks when selecting a running mate, finally picking Harris.

The calendar is also conspiring against the unveiling of a long list of staff members, with Biden expected to honor Veterans Day on Wednesday.

But for his staff, the decisions carry some urgency. The final paychecks from the campaign will come soon, according to one staff member, though health-care coverage may extend through the end of the year. Some key staffers are expected to move as early as this week to the Biden transition team.

Several longtime aides on the campaign are widely expected to be headed to the White House as influential advisers.

Two of those most frequently mentioned are Mike Donilon and Steve Ricchetti, veteran Biden advisers who are well positioned to land influential positions inside the White House, according to people with knowledge of the internal dynamics. Those people spoke on the condition of anonymity to recount private conversations.

Both men played significant roles in Biden’s campaign, helping direct strategy, operations and major decisions, and are considered two of his closest confidants.

Should Biden tap them for top roles, the decision would be among the first concrete signs that he will continue to rely, at least in part, on the old guard of strategists who have guided him for years. Another oft-mentioned name is Ron Klain, who is seen by many in the Biden orbit as a potential White House chief of staff.

At the same time, Biden has vowed to staff an administration that looks like the country, and he is coming under pressure to ensure that his team is diverse. Donilon, Ricchetti and Klain are all White men.

The people with knowledge of the internal dynamics stressed that the situation was fluid and final decisions had not yet been made.

Donilon was the chief strategist for Biden’s campaign and was the lead architect at the staff level on major speeches, including Biden’s October address in Gettysburg, Pa.

Ricchetti served as campaign chairman and was Biden’s chief of staff when he was vice president. Before joining Biden’s staff, Ricchetti helmed a public affairs and lobbying firm.

“The Biden-Harris transition has not made any personnel decisions at this time,” said transition spokesman Cameron French.

The top staffers whom Biden trusts cut significantly different profiles than members of Trump’s team, many of whom gained their White House jobs via television appearances.

In contrast, most of the aides who populate Biden’s inner circle are famously camera-shy and largely avoid efforts to take credit for decisions.

Some staffers not going to the White House immediately will help set up a presidential inaugural committee that will oversee the Jan. 20 transfer of power and associated festivities.

The pandemic raises the possibility that the traditional ceremonies, which draw thousands of supporters to the Mall, may have to be reimagined. The people with internal knowledge said it was possible that Rufus Gifford might chair the inaugural committee, though they were not aware of any final decisions. Gifford served as deputy campaign manager and has been a longtime Democratic fundraiser whom President Barack Obama tapped as ambassador to Denmark.

Holding the event safely amid the pandemic will be difficult, some Biden allies acknowledge, but they have said it’s important to preserve some sense of grandeur given Trump’s refusal to concede.

“It’s easier to scale back than scale up,” Sen. Roy Blunt (R-Mo.), who chairs the Joint Congressional Committee on Inaugural Ceremonies, said Sunday on ABC’s “This Week.” He said that a “full-scale inauguration” is being planned.

Seung Min Kim, Paulina Firozi and Paul Kane contributed to this report.