WASHINGTON — His fellow Democrats are red hot with rage after the assault on the Capitol, but President-elect Joseph R. Biden Jr. has maintained a studied cool, staying largely removed from the searing debate that culminated on Wednesday with President Trump’s impeachment and keeping his focus on battling a deadly pandemic, reviving a faltering economy and lowering the political temperature.

Hours after the vote in the House to impeach Mr. Trump for a second time, Mr. Biden denounced what he called a violent attack on the Capitol and the “public servants in that citadel of liberty.” He said a bipartisan group of lawmakers had condemned the violence by following “the Constitution and their conscience.”

But he also pledged to ensure that Americans “stand together as a nation” when he becomes president next week, exhibiting the deliberate approach to politics that became the trademark of his march to the White House.

“This nation also remains in the grip of a deadly virus and a reeling economy,” he said in a statement. “I hope that the Senate leadership will find a way to deal with their Constitutional responsibilities on impeachment while also working on the other urgent business of this nation.”

Rather than step up to lead his party’s effort to hold Mr. Trump accountable, Mr. Biden has deferred to Speaker Nancy Pelosi and other Democrats in the House and Senate. He has spent the past week honing policy proposals and introducing new appointees while delivering a carefully calibrated, above-the-fray message. “What the Congress decides to do is for them to decide,” he said about impeachment two days after the attacks.

Mr. Biden’s emphasis on the governing challenge ahead is based on a belief that the nation is in a devastating crisis and that requires him to prioritize keeping Americans healthy in the middle of an increasingly devastating pandemic and restoring the prosperity that has evaporated in its wake. But it also underscores the contrast between his cautious, centrist approach to politics and the seething anger of many elected Democratic officials and voters over Mr. Trump’s assaults on democratic norms and their desire to punish him for it.

The president-elect has made it clear that he intends to work toward repairing the breach in America’s political culture after Mr. Trump’s four tumultuous years in office.

“Too many of our fellow Americans have suffered for too long over the past year to delay this urgent work,” he said in the statement. “I have often said that there is nothing we can’t do, if we do it together. And it has never been more critical for us to stand together as a nation than right now.”

But he will be pursuing a Democratic agenda in a sharply divided Congress at the same time, forcing him into a balancing act that is sure to be especially precarious in his administration’s opening weeks as the Senate again litigates Mr. Trump’s behavior and weighs convicting him.

“I think he looks calm,” said Stuart Stevens, a Republican strategist who helped run Mitt Romney’s 2012 presidential campaign and has become an outspoken critic of Mr. Trump. “Part of this whole moment is a return to normalcy. Having a level-headed president who isn’t rage tweeting and trying to win every news cycle — it’s a hallmark of the Biden people. They’ve been very patient.”

As a candidate, Mr. Biden embraced a strategy that purposely kept him above the fray, refusing to be dragged into the chaotic maelstrom of Mr. Trump’s presidency at every turn.

But what worked to win him the Democratic nomination and the White House may wear thin when he is sworn in next Wednesday at the Capitol amid extraordinary security, the potential for further political unrest and pent-up demand from his own party for legislative victories.

Once in office, Mr. Biden is likely to find it all but impossible to keep issues like impeachment at arm’s length, especially with the spectacle of a Senate trial dominating news coverage and slowing his push to win confirmation for his nominees. Robert Gibbs, who served as President Barack Obama’s first press secretary, recalled how the White House struggled to maintain their campaign’s messaging discipline in the first days of the administration in 2009.

“One minute you can decide what you want to comment on,” Mr. Gibbs said. “The next minute, you not only don’t get to decide, but you’re responsible for it all.”

The risk for Mr. Biden is that a determined effort to keep his focus on a return to normalcy comes to be seen as detached from a moment that does not feel at all normal.

On the House floor on Wednesday, Ms. Pelosi called Mr. Trump “a clear and present danger to the country” and a handful of Republicans warned of “a grave danger” from the sitting president and insisted “we cannot wait a moment longer” to remove him from office.

By contrast, in the week since Mr. Trump’s supporters stormed the Capitol, Mr. Biden has introduced members of his cabinet, urged an increase in the minimum wage, pledged to support small businesses and vowed action on the pandemic. Yet while he made clear his disdain and repeated his belief that the current president is not fit to hold office — and ripped Republicans like Senator Ted Cruz of Texas for their roles in promoting baseless claims of widespread election fraud — Mr. Biden sidestepped questions about whether Mr. Trump should be impeached and convicted.

On Wednesday, even as lawmakers weighed whether to make Mr. Trump the first president to be impeached twice, Mr. Biden’s transition team sent out summaries of meetings involving some of his cabinet nominees, including a “listening session” about environmental justice issues and a “virtual round-table discussion” about education for those with disabilities.

People close to the president-elect say Mr. Biden was horrified by the scene at the Capitol. But he is trapped between competing priorities: holding Mr. Trump accountable for inciting violence against the occupants of a building in which he worked for decades, and quickly moving his agenda through a Congress that is already deeply divided.

Mr. Biden’s candidacy was at the heart of the actions that led to Mr. Trump’s first impeachment. Mr. Trump sought to pressure Ukraine to help undercut Mr. Biden via a convoluted series of events related to work done in that country by Mr. Biden’s son, Hunter.

Yet when Democrats announced their intention to impeach Mr. Trump for the first time in late September 2019, Mr. Biden was slow to embrace a process many of his fellow Democrats considered long overdue. It was only two weeks after Ms. Pelosi initiated proceedings against Mr. Trump that Mr. Biden explicitly endorsed them.

That approach was partly a campaign strategy, devised specifically to counter Mr. Trump’s all-consuming tactics. But it was also a reflection of Mr. Biden’s temperament and his broader political instincts.

As a creature of the Senate for more than 30 years, many of them during an era of relative bipartisan comity on Capitol Hill, Mr. Biden was a deal maker who prided himself on working with Republicans, honored Senate traditions, and was less inclined than many of his colleagues to surf partisan passions. As a young senator in 1974, Mr. Biden was even wary of the impeachment of President Richard M. Nixon.

“I don’t know what’s in his head, but I suspect that because of where his body has been over the last several decades, he would have mixed feelings” about the impeachment now underway, said Representative James E. Clyburn, the House Democratic whip and a close adviser to Mr. Biden. “He is an institutionalist.”

Mr. Clyburn said that the president-elect did not want to be distracted from the challenges that would confront the country as soon as he succeeded Mr. Trump in the Oval Office.

“He would love to get on with getting the country back on track, and with that I agree,” said Mr. Clyburn, who voted to impeach Mr. Trump on Wednesday. He said that Mr. Biden understood how “egregious” Mr. Trump’s behavior was and was “seeking a level of comfort” that balanced punishing the president with turning the page on the Trump era.

Mr. Obama, too, faced hard decisions as he assumed office in 2009 about how much time and energy to devote to litigating the recent past, and holding officials from the George W. Bush administration accountable.

In April of that year, Mr. Obama approved the public release of Bush White House memos authorizing the use of torture against terrorist suspects. But in a long and Solomonic statement, Mr. Obama called for “reflection, not retribution” on a subject that had some Democrats calling for war crimes prosecutions.

But the likelihood of Washington being consumed by a Senate trial in the opening days of Mr. Biden’s administration will make especially acute the tension between holding his predecessor accountable and a focus on the nation’s other pressing challenges.

“To the degree that the Senate is consumed by the first,” said David Axelrod, Mr. Obama’s chief political adviser in 2009, “he may fear that it’ll be harder to move on his own appointments and agenda.”