WASHINGTON — With a nation on edge, ravaged by disease, hammered by economic collapse, divided over lockdowns and even face masks and now convulsed once again by race, President Trump’s first instinct has been to look for someone to fight.

Over the last week, America reeled from 100,000 pandemic deaths, 40 million people out of work and cities in flames over a brutal police killing of a subdued black man. But Mr. Trump was on the attack against China, the World Health Organization, Big Tech, former President Barack Obama, a cable television host and the mayor of a riot-torn city.

As several cities erupted in street protests after the killing of George Floyd, some of them resulting in clashes with the police, Mr. Trump made no appeal for calm. Instead in a series of tweets and comments to reporters on Saturday, he blamed the unrest on Democrats, called on “Liberal Governors and Mayors” to get “MUCH tougher” on the crowds, threatened to intervened with “the unlimited power of our Military” and even summoned his own supporters to mount a counterdemonstration.

The turmoil came right to Mr. Trump’s doorstep on Friday night as hundreds of people protesting Mr. Floyd’s death and the president’s response gathered outside the White House. Some threw bricks and bottles at Secret Service and United States Park Police officers, who responded with pepper spray. The image of the White House surrounded by police in riot gear fueled the sense of a nation torn apart.

Mr. Trump praised the Secret Service for being “very cool” and “very professional” but assailed the Democratic mayor of Washington for not providing city police officers to help. While governors and mayors have urged restraint, Mr. Trump seemed more intent on taunting the protesters, bragging about the violence that would have met them had they tried to get onto White House grounds.

“Big crowd, professionally organized, but nobody came close to breaching the fence,” the president wrote on Twitter. “If they had they would have been greeted with the most vicious dogs, and most ominous weapons, I have ever seen. That’s when people would have been really badly hurt, at least. Many Secret Service agents just waiting for action.”

His suggestion that his own supporters should come to the White House on Saturday foreshadowed the possibility of a clash outside his own doors. “Tonight, I understand, is MAGA NIGHT AT THE WHITE HOUSE???” he wrote on Twitter, using the acronym for his first campaign slogan, “Make America Great Again.”

Asked about the tweet later, he denied encouraging violence by his supporters. “They love African-American people,” he said. “They love black people. MAGA loves the black people.”

Mayor Muriel E. Bowser of Washington responded in kind on Saturday morning, saying her police department will protect anyone in Washington, including the president, but called him a source of division. “While he hides behind his fence afraid/alone, I stand w/ people peacefully exercising their First Amendment Right after the murder of #GeorgeFloyd & hundreds of years of institutional racism,” she wrote. “There are no vicious dogs & ominous weapons. There is just a scared man. Afraid/alone …”

The days of discord have put the president’s leadership style on vivid display. From the start of his ascension to power, Mr. Trump has presented himself as someone who seeks conflict, not conciliation, a fighter, not a peacemaker. That appeals to a substantial portion of the public that sees in him a president willing to take on an entrenched and entitled establishment.

But the confluence of perilous health, economic and now racial crises has tested his approach and left him struggling to find his footing just months before an election in which polls currently show him behind.

“The president seems more out-of-touch and detached from the difficult reality the country is living than ever before,” said Carlos Curbelo, a former Republican congressman from Florida who has been critical of Mr. Trump. “At a moment when America desperately needs healing, the president is focused on petty personal battles with his perceived adversaries.”

Such a moment would challenge any president, of course. It has been a year of national trauma that started out feeling like another 1998 with impeachment, then another 1918 with a killer pandemic combined with another 1929 given the shattering economic fallout. Now add to that another 1968, a year of deep social unrest.

It is fair to say that 2020 has turned out to be a year that has frayed the fabric of American society with an accumulation of anguish that has whipsawed the country and its people. But in some ways, Mr. Trump has become a combatant on one side of the divide rather than a mender of it, a totem for the nation’s polarization.

“I am daily thinking about why and how a society unravels and what we can do to stop the process,” said Timothy Naftali, a presidential historian at New York University. “The calamity these days is about more than Trump. He is just the malicious con man who lives to exploit our vulnerabilities.”

As the nation has confronted a coronavirus pandemic at the same time as the greatest economic catastrophe since the Great Depression, whatever unified resolve that existed at the beginning of the twin crises quickly evaporated into yet another cultural clash. And the president has made everything into just another partisan dispute rather than a source of consensus, from when and how to reopen to whether to wear a mask in public.

Mr. Trump led no national mourning as the death toll from the coronavirus passed 100,000 beyond lowering the flags at the White House, posting a single tweet and offering a passing comment on camera only when asked about it. Rather than seek agreement on the best and safest way to reopen the country, he threatened to “override” governors who prevented places of worship from resuming crowded services.

“Crisis leadership demands much more from the White House than irresponsible threats on social media,” said Meena Bose, director of the Peter S. Kalikow Center for the Study of the American Presidency at Hofstra University.

Mr. Trump’s initial response to the rioting in Minneapolis, where a police officer has been charged with murder after kneeling on Mr. Floyd’s neck for nearly nine minutes as he cried out that he could not breathe, underscored the president’s most instinctive response to national challenges. Threatening to send in troops, he wrote early Friday morning that “when the looting starts, the shooting starts.”

Only after a cascade of criticism did he try to walk it back, posting a new tweet 13 hours later, suggesting that all he had meant was that “looting leads to shooting” by people in the street.

“I don’t want this to happen, and that’s what the expression put out last night means,” he said, a reformulation that convinced few if any of his critics.

Democrats have decried the president’s handling of the multiple crises confronting the nation. “America is reeling from 100,000 deaths and rising. Forty million have filed for unemployment. Our communities are hurting from senseless murders and years of racism and injustice,” Senator Chuck Schumer, Democrat of New York and the minority leader, said on Friday. “But President Trump is only interested in scapegoating and divisiveness when he should be leading.”

Even some of Mr. Trump’s usual allies were distressed at the original shooting tweet. Geraldo Rivera, the television and radio host who often spends time with Mr. Trump at the president’s Mar-a-Lago club in Florida, decried “the recklessness” of that message and called on the president “to self-censor himself.”

“Come on, what is this, sixth grade?” Mr. Rivera said on Fox News. “You don’t put gasoline on the fire. That’s not calming anybody.” He added: “All he does is diminish himself.”

But many of the president’s defenders rejected the idea that he had mishandled the crises, pressing the argument that Democrats and the news media were to blame for the turmoil in the streets, which spread from Minneapolis to New York, Atlanta, Washington, Louisville, Portland and other cities.

“Keep track of cities where hundreds of millions of dollars in property damage and serious injuries and death will take place,” Rudolph W. Giuliani, the former New York mayor who has served as Mr. Trump’s personal lawyer, wrote on Twitter on Friday night. “All Democrat dominated cities with criminal friendly policies. This is the future if you elect Democrats.”

Bernard B. Kerik, the former New York City police commissioner who was pardoned by Mr. Trump for tax fraud earlier this year, amplified the point on Twitter. “It should be no surprise that every one of these cities that the anarchist have taken over, are the same cities run by leftist Democrats with the highest violence, murder and poverty rates,” he wrote on Twitter. “They can’t handle their cities normally, so how are they going to deal with this?”

Mr. Trump, who this past week retweeted a video of a supporter saying that “the only good Democrat is a dead Democrat” (though the supporter insisted he meant that in a political sense), picked up the theme on Friday night and again on Saturday morning.

After crowds attacked CNN’s Atlanta headquarters with rocks, the president offered no sympathy or condemnation. Instead, he made clear he thought it was just deserts for a network that has aggravated him so much, retweeting a message that said: “In an ironic twist of fate, CNN HQ is being attacked by the very riots they promoted as noble & just.”

In her typical appearances on Fox News, Jeanine Pirro, a former Republican district attorney, reserves her highest dudgeon for castigating liberals and lamenting the demise of law and order.

But on Friday’s “Fox & Friends,” Ms. Pirro’s voice nearly broke as she described the agonizing final moments of George Floyd, the black man who died after a Minneapolis police officer ignored his pleas and pinned him to the ground during a routine stop.

“George Floyd was begging, saying he couldn’t breathe, saying please, please,” Ms. Pirro told viewers. “This man who put his knee on the neck of George Floyd does not deserve to be free in this country.”

Even right-wing stars like Rush Limbaugh hedged their assessments early on, as the officer’s lethal force drew more condemnation in some corners of the right than the ensuing riots and the burning of a police precinct. “I can’t find a way to justify it,’’ Mr. Limbaugh said of the officer’s actions.

The chilling circumstances of Mr. Floyd’s death — particularly the graphic, indisputable video of his arrest — have, at least for now, posed a political quandary among some conservative politicians, media stars and President Trump, whose usual instinct is to focus on blaming liberals for promoting lawlessness.

The ongoing protests in Minneapolis and around the country may still alter conservative views. On Fox News on Friday night, Tucker Carlson began his show with a graphic calling the Minnesota protesters “Criminal Mobs,” and wondered aloud why Republicans were not reacting more intensely against the violence in Minneapolis. Sean Hannity and Laura Ingraham condemned the demonstrators for, in Mr. Hannity’s words, “exploiting” Mr. Floyd’s death.

The law enforcement community is one of Mr. Trump’s most loyal constituencies, and he and his allies are in uncharted territory as they weigh expressions of solidarity with the nation’s police forces against grappling with the horror of Mr. Floyd’s death.

Initially, Mr. Trump issued a brutal law-and-order message early Friday morning, tweeting, “When the looting starts, the shooting starts.” His implication that protesters should be shot by law enforcement drew enormous blowback from Democratic leaders and other critics; some 14 hours later, he said his tweet had been misinterpreted, and later talked about the “good people” who were demonstrating in Mr. Floyd’s honor.

“They were protesting for the right reasons,” Mr. Trump told reporters at the White House on Friday evening, in relatively subdued remarks for a president best-known for bluster and vitriol. “They were protesting in honor of a man, George Floyd, where something happened that shouldn’t have happened.”

Aides to Mr. Trump said on Friday they saw little advantage in further inflaming a situation that had already turned violent across several cities. They were mindful, too, of avoiding any further alienation of African-American voters, ahead of an election where even marginal shifts in support could help him eke out a victory in November.

By Saturday morning, however, Mr. Trump had shifted tone again, writing in a tweet that any “protesters” — he put the word in quotes — who behaved out of line at the White House would face a “hard” response by Secret Service and “the most vicious dogs, and most ominous weapons, I have ever seen.”

Casting itself as the upholder of law-and-order has been a perennial Republican Party strategy in times of racial disharmony and social unrest, from the 1967 riots in Detroit and Newark to Ferguson, Mo., in 2014.

But the stark footage of a white police officer kneeling on the neck of Mr. Floyd as he pleaded and moaned “I can’t breathe” produced an unusual moment when those on either side of the nation’s split-screen politics were, publicly at least, evincing a common cause.

The moment may be fleeting.

In an appearance on Fox News on Friday evening, Senator Ted Cruz of Texas faced tough questions from Mr. Carlson — one of Mr. Trump’s favorite anchors — about why the senator was quick to denounce Mr. Floyd’s death as “a horrific act of police brutality.”

“In this instance, we have a video of the incident,” Mr. Cruz said. “What we saw was wrong.”

Mr. Carlson pushed back, asking Mr. Cruz if he believed it was fair to bring a murder charge against the officer who arrested Mr. Floyd.

“Why doesn’t anybody stand up for the rest of us, for civilization?” Mr. Carlson asked.

The exchange, between two pillars of the conservative establishment, threw into relief the tensions that had played out on cable TV and talk-radio this week.

On his syndicated radio show on Thursday, Mr. Limbaugh expressed dismay at the actions of the police. “Look, you people in law enforcement know I’m at the top of the list of people who support you and understand how hard your jobs are,” he told listeners. “I still — given all of that, do not … I cannot find a way to explain that. I can’t find a way to justify it. I don’t care what the guy did.”

But Mr. Limbaugh also mocked the Democratic mayor of Minneapolis, Jacob Frey, who had made a tearful plea for unity.

“This is a blue state where this happened; this is a state run by Democrats; this is a state run by leftists,” Mr. Limbaugh told listeners. “Don’t forget, these are the people who have been promising their African-American voters this stuff’s gonna stop for 50 years. They don’t fix anything.”

Senator John Kennedy, the Louisiana Republican, appearing on Fox News on Friday, called Mr. Floyd’s death a “murder,” but he also said “the people who are trying to burn down Minneapolis should be prosecuted to the full extent of the law.”

J. McCauley Brown, the Republican Party chairman in Kentucky, said in an interview that “it’s unfortunate there are some people who are getting violent.” But he called Mr. Floyd’s death “tragic,” adding, “I can understand totally why people are protesting.”

Among some conservatives, condemnation of the Minnesota police officers was often entwined with disdain for perennial targets of the right: big city Democratic politicians, the media, the Black Lives Matter movement and others who conservatives have blamed for helping stoke the violence. On Friday, the Drudge Report blared a headline in capital letters: “Unrest Spreads in U.S.A.”

The president’s campaign manager, Brad Parscale, seized on the backlash to Mr. Trump’s “looting” tweet to attack “the media, Joe Biden, and the Democrats,” ticking off a triumvirate of Republican boogeymen.

In a campaign statement, Mr. Parscale wrote that Minneapolis was “in chaos” and, without evidence, accused Democrats and the media of capitalizing on the tragedy as “a political opportunity and a chance to make money” — both offenses that Mr. Trump and Mr. Parscale himself are often accused of.

Donald Trump Jr., the president’s son, wrote on Twitter that “what happened to George Floyd was disgusting.” But he quickly added: “There’s never an excuse for the type of violent riots unfolding now. No American should ever have to watch their own community burn to the ground.”

For years now, some Republicans have sought to turn the issue of racial inequality and injustice to their political advantage. The president — who famously courted African-Americans to take a chance on him in 2016 by asking “What the hell do you have to lose?” — has long believed that he could appeal to black voters by blaming Democrats for chronic problems in predominantly black communities like poverty, crime and poor schools.

The president’s decision to call the Floyd family and express his condolences suggested that he did not view this episode as the kind of racially fraught cultural battlefront he would otherwise barrel into.

And with the nation on edge, the gravity of the situation had not been lost on Mr. Trump’s team. At a Friday morning meeting, two White House aides, Brook Rollins and Ja’Ron Smith, argued it would be tone-deaf for Mr. Trump to roll out new initiatives, even those related to the coronavirus, in the next few days that did not pertain to the fallout from Mr. Floyd’s death.

All that could change, especially if the situation continues to deteriorate in cities like Minneapolis, and if cable news — closely monitored by Mr. Trump — is filled with images of violence and carnage.

“Give it 24 or 48 hours,” Charlie Sykes, a longtime conservative radio star who now opposes Mr. Trump, said in an interview. “This is the president who ran as the law and order president. It is almost irresistible.”

Mr. Sykes said it was inevitable that the conservative media outrage machine would ramp up as the right-wing playbook reasserts itself, after the short-term caution in the aftermath of a horrific murder caught on tape.

Indeed, by Friday evening, Mr. Hannity was warning viewers about “radical rioters exploiting this death of Mr. Floyd, committing crimes, justifying crimes, threatening more violence.” To analyze the protests, Ms. Ingraham brought on a provocative guest: Mark Fuhrman, the former Los Angeles police detective infamous for his role in the O.J. Simpson murder trial.

For now, Republican officials continue to see two problems at hand, each of which they believe is serious and urgent. “I understand the protesters are frustrated and they want swift justice, and I feel that for them,” Laura Cox, Republican Party chairwoman in Michigan, said in an interview.

But, Ms. Cox added, “When it starts to be about breaking into police precincts, that’s problematic.”