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On a fifth night of unrest in Minneapolis, protesters met a more aggressive response.

Protesters who took to the streets in Minneapolis for the fifth straight night on Saturday met a more determined response from police officers and National Guard troops, as demonstrations escalated in dozens of cities across the country — an outpouring of national anger sparked by the death of a black man in police custody.

Soon after an 8 p.m. curfew took effect, the police in Minneapolis began arresting protesters and firing tear gas and other projectiles toward crowds, and the National Guard used a helicopter to dump water on a burning car.

The forceful response reflected the desire of authorities to halt the violent protests that have spread nationwide since George Floyd, 46, died after being pinned down by a white Minneapolis police officer. There were still reports of violence and destruction: a fire on the roof of a shopping mall, a person who shot a gun at officers, and a group of people throwing items at the polic. But state officials said around 11 p.m. local time that they were encouraged by the smaller crowds and apparent decrease in damage. Much of the city was empty shortly after midnight.

But even as aerial videos from Minneapolis showed police officers largely keeping demonstrators at bay, other cities were being overwhelmed, despite hastily imposed curfews.

Mayors ordered people of the streets in many of the nation’s largest cities, including Los Angeles, Chicago, Philadelphia and Miami. And governors in at least eight states, including Georgia, Kentucky, Ohio, Colorado and Tennessee, called up National Guard troops in an attempt to impose order, often with little success.

In Tennessee, the building that houses Nashville’s City Hall was set on fire. Two police vans in New York City were filmed plowing into protesters. In Washington, demonstrators set fires and smashed the windows of buildings near the White House. The police in Indianapolis said three people had been shot during the protests — not by police officers — including one person who was killed. And in Philadelphia, the Police Department said at least 13 officers had been injured during protests.

The demonstrations continued to escalate on Friday and Saturday even after Derek Chauvin, the former Minneapolis police officer who was recorded kneeling on Mr. Floyd’s neck until he lost consciousness, was charged with third-degree murder.

President Trump has harshly criticized the unrest, and Attorney General William P. Barr warned on Saturday that people inflicting the destruction could face federal charges. Gov. Tim Walz of Minnesota said the people defying curfews and trying to instigate police were no longer protesting police brutality, but rather seeking to exploit Mr. Floyd’s death for their own political motives.

Protests escalated nationwide throughout Saturday, prompting many cities to impose curfews.

Tens of thousands of people were in the streets across the United States on Saturday night, as demonstrations stretched from coast to coast in a national paroxysm of rage that saw buildings set on fire, businesses looted and an aggressive response from the authorities.

Protests have taken place in at least 75 cities and have reached the gates of the White House in the days since the death of Mr. Floyd in Minneapolis. The imposition of curfews by mayors appeared to be more widespread on Saturday than at any time since the aftermath of the assassination of Martin Luther King Jr. in 1968.

• In Indianapolis, one person was killed and three others were injured when a gunman fired shots at a protest, the police said.

• In Chicago, protesters scuffled with police on Saturday afternoon, burning at least one flag and marching toward the Trump International Hotel and Tower before dispersing. About 3,000 people took part in the protests, according to local news reports. Some vandalized police vehicles and left spray-painted buildings in their wake.

• In Los Angeles, Mayor Eric M. Garcetti issued a curfew, a day after the police made more than 500 arrests. Police used batons and rubber bullets to disperse crowds and Gov. Gavin Newsom activated the National Guard.

• In San Francisco, Mayor London Breed issued a curfew as demonstrators arrived outside her home to protest.

• In Miami-Dade County, Fla., Mayor Carlos Gimenez ordered a countywide curfew beginning at 11 p.m. after at least one police car was set ablaze near the Miami Police Department headquarters. Tear gas was also used to disperse crowds on Saturday evening in Jacksonville and Orlando.

• In Washington, the National Guard was deployed outside the White House, where chanting crowds clashed with the Secret Service and attacked a Fox New reporter. Fires were set in Lafayette Park, just steps from the White House.

• In Philadelphia, at least 13 police officers were injured when protesters began setting fires and became violent.

• In New York City, thousands of demonstrators took to the streets for a third day, gathering at marches in Harlem, Brooklyn, Queens and outside Trump Tower in Midtown Manhattan. In the late afternoon, protesters in the Flatbush section of Brooklyn confronted the police in a series of street melees, hurling empty bottles and pieces of debris at officers who responded with billy clubs and pepper spray. A video showed a police car driving into a crowd.

• In Richmond, Va., two police officers at the State Capitol were hospitalized with leg injuries after being struck by a baseball bat and a beer bottle, The Richmond Times-Dispatch reported. Earlier, the police fired tear gas at protesters, some of who launched fireworks and smashed windows.

Police and protesters clashed as flames rose on the streets outside the White House.

The turmoil was on display a short distance from the White House, where President Trump had called earlier in the day for his supporters to rally. Instead, hundreds of protesters mobilized on the streets of the nation’s capital as tensions ratcheted higher.

Demonstrators hurled projectiles, including water bottles, fireworks and bricks, and wrested barricades from the police, who responded by lobbing canisters of tear gas into the crowd. Buildings up and down the streets near the White House were sprayed with graffiti, including the entrance of the Hay-Adams, a luxury hotel.

Nearby, scaffolding on a construction site behind the United States Chamber of Commerce could be seen on fire. The windows at the entrance of the building were smashed.

Around 11 p.m., two cars were set ablaze on an adjacent block, and a local bank was vandalized, its windows broken and the numbers “666” sprayed across the front.

As police officers moved to secure the block, a Chevy Suburban was engulfed in a plume of black smoke; trees nearby were on fire. The crowds retreated into Farragut Square to regroup as helicopters circled overhead, and some split off back toward the White House.

President Trump had made a series of statements throughout the day that did little to tamp down the outrage nationwide. Speaking on the South Lawn of the White House, he criticized the authorities in Minnesota for allowing protests to turn violent, and offered the help of the military to contain further demonstrations.

In a series of tweets, he called demonstrators who gathered at the White House on Friday night “professionally managed so-called ‘protesters’” and suggested that his supporters would meet them. “Tonight, I understand, is MAGA NIGHT AT THE WHITE HOUSE???”

Later Saturday, speaking from the Kennedy Space Center in Florida after observing the launch of a manned SpaceX rocket, Mr. Trump blamed the unrest in cities across the country on “Antifa and other radical left-wing groups,” drawing a distinction between “peaceful protesters” and other, more violent demonstrators.

“What we are now seeing on the streets of our cities has nothing to do with justice or with peace,” Mr. Trump said. “The memory of George Floyd is being dishonored by rioters, looters and anarchists.”

Former Vice President Joseph R. Biden Jr., the presumptive Democratic presidential nominee, released a statement early Sunday morning appealing for calm.

“We are a nation in pain, but we must not allow this pain to destroy us,” he wrote. “We are a nation enraged, but we cannot allow our rage to consume us. We are a nation exhausted, but we will not allow our exhaustion to defeat us.”

Minnesota’s governor activated all National Guard troops, but declined the Army’s offer to deploy military police.

Gov. Tim Walz of Minnesota activated thousands of additional National Guard troops to send to Minneapolis but declined the Army’s offer to deploy military police units, as days of protests over the death of Mr. Floyd threatened to boil over even further on Saturday.

Mr. Walz, a Democrat, acknowledged that officials had underestimated the demonstrations in Minneapolis, where despite a newly issued curfew, people burned buildings and turned the city’s streets into a smoldering battleground on Friday night. He compared the havoc to wars that Americans have fought overseas, and said he expected even more unrest on Saturday night.

“What you’ve seen in previous nights, I think, will be dwarfed by what they will do tonight,” he said.

Pentagon officials said that Defense Secretary Mark Esper and General Mark Milley, the chairman of the Joint Chiefs of Staff, spoke Friday with Mr. Walz, to express “willingness” to deploy military police units. The governor declined the offer, the officials said, and has since activated all of the state’s National Guard troops, up to 13,200.

Nonetheless, the U.S. Northern Command has put several military police units on four-hour status, which means they could be ready to deploy in four hours, as opposed to a day.

Commissioner John Harrington of the Minnesota Department of Public Safety said that there had been “tens of thousands” of people in the streets on Friday, more than any other night since Mr. Floyd’s death on Monday set off a wave of protests that have become increasingly destructive across the country.

Mayor Jacob Frey of Minneapolis, looking weary after four days of outrage in his city, pleaded with residents to go home and stop burning down the local businesses that he said were even more vital in the middle of a pandemic.

“You’re not getting back at the police officer that tragically killed George Floyd by looting a town,” Mr. Frey said. “You’re not getting back at anybody.”

At least four people have been killed in violence connected with the protests.

One person was killed and three others were injured when a gunman fired shots at a protest in Indianapolis early Sunday morning, bringing to at least four the total number of people killed since Wednesday in violence connected with the protests.

The authorities were also investigating a possible connection with the shooting death of a federal officer in California.

The officer, a contract security guard for the Department of Homeland Security, was shot and killed outside a federal courthouse in Oakland, Calif., on Friday night as demonstrations in the city turned violent, with protesters setting fires, destroying property and clashing with the police.

Ken Cuccinelli, the Department of Homeland Security’s acting deputy secretary, called the attack an act of “domestic terrorism,” but the state’s governor cautioned against connecting the shooting with the protests.

“No one should rush to conflate this heinous act with the protests last night,” said Gov. Gavin Newsom, a Democrat, in a statement.

Elsewhere, people were killed when once-peaceful protests descended into violence.

The authorities in Minneapolis on Friday identified Calvin L. Horton Jr., 43, as the victim in a shooting outside a pawnshop that was being looted.

Also on Friday in Detroit, a 21-year-old man was shot to death while sitting in his car near Cadillac Square, as hundreds of protesters swarmed the streets. The police said the gunman may have known and targeted the victim and used the chaos of the demonstrations as a cover.

Early Saturday morning in St. Louis, a man was killed after protesters blocked Interstate 44, set fires and attempted to loot a FedEx truck. The man was killed, the police said, when he became caught between the truck’s two trailers as the driver attempted to wend his way through the protest.

Officials blame outsiders for stoking violence, but have little evidence.

Officials in Minnesota and Washington are claiming that outside groups are undermining the protests in Minneapolis, using them as a cover to set fires, loot stores and destroy property. But they disagree on whether far-left or far-right groups are to blame and have not offered evidence to substantiate their claims.

On Saturday, Governor Walz said the “best estimate” suggested that 80 percent of those arrested at the protests were not from the state. “I’m not trying to deflect in any way. I’m not trying to say there aren’t Minnesotans amongst this group,” Mr. Walz said. But “the vast majority,” he said, are from outside the state.

KARE, a Minneapolis television station, found that such claims may not be accurate. The station reviewed all of the arrests made by Minneapolis-based police agencies for rioting, unlawful assembly and burglary-related crimes from Friday to Saturday and found that 86 percent of those arrested listed a Minnesota address.

The mayor of St. Paul, Melvin Carter, on Saturday retracted his claim that “every single person” arrested on Friday night was from out of state. A spokesman said the mayor later learned that “more than half” are from Minnesota.

John Harrington, commissioner of the Minnesota Department of Public Safety, said the authorities were analyzing those arrested, trying to understand what online platforms they have used and who they were associated with.

“We have seen things like white supremacist organizers who have posted things on platforms about coming to Minnesota,” Mr. Harrington said. “Is this organized crime? Is this an organized a cell of terror? Where is the linkage?”

Mayor Frey also blamed outsiders for the violence. “We are now confronting white supremacists, members of organized crime, out of state instigators, and possibly even foreign actors to destroy and destabilize our city and our region,” he wrote on Twitter.

On Saturday, President Trump insisted that the protesters were far-left extremists. “The memory of George Floyd is now being exploited by rioters, looters and anarchists,” he said.

Attorney General William P. Barr echoed the claim.

“In many places it appears the violence is planned, organized and driven by anarchic and left extremist groups, far-left extremist groups, using Antifa-like tactics, many of whom travel from outside the state to promote the violence,” he said.

Residents also say that Minneapolis has a core group of white anarchists. A man known as the Umbrella Man, dressed in all black and carrying a black umbrella, who appears to be white, was filmed breaking windows at an AutoZone store.

Tension rose at protests in Los Angeles, where memories of Rodney King are still raw.

The protest on Los Angeles’s affluent West Side began peacefully on Saturday and stayed that way for nearly three hours. Activists handed out water and food, and a crowd marched on Beverly Boulevard, chanting slogans against police brutality and waving placards.

And then it took a violent turn.

Suddenly a police car was smashed and on fire, black smoke billowing into the blue sky. A young man threw a skateboard at a police officer, and frightened men and women rushed away in every direction. Police helicopters hovered overhead, and convoys of police S.U.V.s raced to the scene.

As tensions rose on the fourth day of protests in Los Angeles over the death of George Floyd, Mayor Eric M. Garcetti declared an 8 p.m. curfew.

“Go home,” Mr. Garcetti said. “Let us put the fires out. Let us learn the lessons. Let us re-humanize each other.”

But later in the evening, looting was reported at a Nordstrom store at The Grove, an upscale mall near the area of the protest, and a small fire was burning outside.

In San Francisco, a march drew about 1,000 people but remained peaceful, The San Francisco Chronicle reported. In Oakland, Mayor Libby Schaaf called on demonstrators to stay home after violent demonstrations on Friday.

In Sacramento, police officers surrounded the State Capitol as protesters pelted them and their horses with oranges and water bottles.

Before the mayhem started in Los Angeles on Saturday afternoon, several hundred people reflecting the diversity of the city — white, black, Latino, Asian-American — had protested peacefully.

The death of Mr. Floyd and the unrest it has provoked has tugged at painful memories in Los Angeles of the Rodney King beating in 1991 and the riots that occurred the next year after the acquittal of the four police officers involved in the case.

Reporters find themselves the targets of violence from protesters and the police.

A freelance photographer who was shot in the eye while covering the protests in Minneapolis on Saturday was of one of several journalists who have been attacked, arrested or otherwise harassed while covering the protests that have erupted nationwide.

With trust in the news media lagging, journalists have found themselves the target of ire on both sides of a deeply politicized crisis.

A television reporter in Louisville, Ky., was hit by a pepper ball on live television by an officer who appeared to be aiming at her.

Outside the White House, protesters attacked Leland Vittert, a Fox News correspondent and his crew, taking the journalist’s microphone and striking him with it.

In Atlanta, masses of protesters on Friday night convened on the CNN headquarters, where they broke through the front door, lobbed fireworks and vandalized the building. Earlier in the day, Omar Jimenez, a reporter for the network, was detained as he reported on live television.

“I was aiming my next shot, put my camera down for a second, and then my face exploded,” said Linda Tirado, the photojournalist. “I immediately felt blood and was screaming, ‘I’m press! I’m press!’”

The Reporters Committee for Freedom of the Press logged about 10 different incidents that ranged from assaults to menacing in Phoenix, Indianapolis, Atlanta and Minneapolis.

“With the unraveling of civil peace around the country, reporters are perceived as a target by both the police and the protesters,” said Bruce Brown, the executive director of the Reporters Committee, “and that is an extremely frightening place to be.”

An anguished nation watched the unrest with a mix of hope and horror.

The mass demonstrations, some peaceful, some destructive, touched off an anguished debate on Saturday among commentators, pastors and scholars about the role of protest in forcing political and social change in America.

In the pages of the nation’s newspapers and on social media, some watched in horror and others with a sense of hope as protesters took to the streets following Mr. Floyd’s death.

The singer Selena Gomez said she had spent the last 24 hours “trying to process this all.”

“Nothing anyone says can take back what has happened,” she wrote on Twitter. “But we can and must all make sure to take action. Too many black lives have been taken from us for far too long.”

Shana L. Redmond, a scholar of music, race and politics at U.C.L.A.’s Herb Alpert School of Music, described receiving tearful calls from loved ones in Minneapolis with “tears running too fast to pause at sadness.”

“They are hot with rage and anger at the condition of Black people in that place and in this world,” she wrote on Twitter. “This is not a drill. This is our terrifying, murderous present. #MinneapolisRebellion.”

Some who sympathized with the protesters voiced concern that the destruction could undermine the goal of forcing social change.

“I understand our frustration, rage and anger but it’s of no benefit when we hurt ourselves in the process,” Jamal H. Bryant, the pastor of New Birth Missionary Baptist Church in Lithonia, Ga., wrote on Twitter. “I urge adamantly for the fixing of this corrupt justice system and I pray profusely for the black businesses adversely affected!”

Senator Tim Scott of South Carolina, the only black Republican in the Senate, who has called for the arrest of all four officers involved the arrest of Mr. Floyd, urged calm.

“I know well the anger and frustration felt throughout communities of color right now,” he wrote on Twitter. “But violence is not the answer. Violence takes the focus off #GeorgeFloyd and the real issues at hand, and gives those who prey on division more fuel. Make your voices heard, not bricks and fire.”

Brian Merchant, an author, noted how the nation was briefly distracted on Saturday by the launch of a rocket built and operated not by NASA but SpaceX, the company founded by the billionaire Elon Musk.

“The symbolism of a billionaire-owned, for-profit space company launching astronauts high above the heads of thousands of people protesting state brutality and oppression amid a global pandemic and economic collapse should not be lost on anyone,” he wrote.

On Blavity, a website geared toward black millennials, an editorial argued that the fires in Minneapolis reflected “the rage of Black protestors fed up seeing the lives of our brothers and sisters robbed by racism.”

“We are fed up because we are forced to fight a pandemic amid a pandemic,” the editorial said. “We are being disproportionately killed by systemic and overt racism at the same time — and are expected to accept these deadly conditions.”

In The Los Angeles Times, an editorial argued that the country should focus should not on the looting but on the repeated instances of the police killing black men.

“And no, police violence does not justify the rampages that erupted in Minneapolis,” the editorial said. “But as the Rev. Martin Luther King Jr. pointed out more than a half-century ago, ‘a riot is the language of the unheard.’”

The officer who pinned Mr. Floyd was charged with murder, and his wife is seeking a divorce.

The intensifying protests came after the authorities announced that the officer who pinned George Floyd to the ground had been arrested and charged with murder on Friday, a development that activists and Mr. Floyd’s family had called for but also said did not go far enough.

The officer, Derek Chauvin, 44, was charged with third-degree murder and second-degree manslaughter, charges that come with a combined maximum sentence of 35 years.

An investigation into the three other officers who were present at the scene remains ongoing.

Mr. Floyd’s relatives have said that had wanted the more serious charge of first-degree murder.

Third-degree murder does not require an intent to kill, according to the Minnesota statute, only that the perpetrator caused someone’s death in a dangerous act “without regard for human life.” Charges of first- and second-degree murder require prosecutors to prove, in almost all cases, that the perpetrator made a decision to kill the victim.

A lawyer for Mr. Chauvin’s wife, Kellie, said that she was devastated by Mr. Floyd’s death and expressed sympathy for his family and those grieving his loss. The case has also led Ms. Chauvin to seek a divorce, the lawyer, Amanda Mason-Sekula, said in an interview on Friday night.

Reporting was contributed by Tim Arango, Mike Baker, Peter Baker, Julian E. Barnes, Nicholas Bogel-Burroughs, Audra D.S. Burch, Helene Cooper, Manny Fernandez, Thomas Fuller, Matt Furber, Russell Goldman, Michael M. Grynbaum, Maggie Haberman, Shawn Hubler, Annie Karni, Michael Levenson, Neil MacFarquhar, Patricia Mazzei, Shawn McCreesh, Sarah Mervosh, Jeremy W. Peters, Frances Robles and Rick Rojas. Research was contributed by Jack Begg.