MINNEAPOLIS — The nation was rocked again Saturday as demonstrators clashed with police from outside the White House gates to the streets of more than three dozen besieged cities, as outrage over the death of George Floyd in Minneapolis traversed a razor’s edge between protest and civic meltdown.

Gov. Tim Walz of Minnesota activated thousands of National Guard troops — up to 13,200 — to control protesters in Minneapolis who turned out in droves for the fifth consecutive night Saturday after burning buildings to the ground, firing guns near the police and overwhelming officers the night before. But he declined the Army’s offer to deploy military police units.

Rallies, looting and unrest expanded far beyond Minneapolis, with protesters destroying police vehicles in Atlanta and New York and blocking major streets in Detroit and in San Jose, California. Crowds in Milwaukee chanted, “I can’t breathe”; and demonstrators in Portland, Oregon, lit a fire inside the Multnomah County Justice Center.

On Saturday, demonstrators amassed outside City Hall in San Francisco, shut down highway traffic in Miami and attempted to topple a statue in Philadelphia. Curfews were imposed in some of America’s largest cities, including Los Angeles, Chicago and Atlanta.

The chaos and rage on such a broad scale evoked the Black Lives Matter demonstrations of recent years; the Los Angeles riots that followed the 1992 acquittal of four police officers charged in connection with the beating of Rodney King the year before; and even the racial strife of the 1960s, when the fury and despair of inner-city African Americans over racism and poverty erupted in scores of cities, reaching a climax in 1967 and 1968, two years that saw more than 150 riots.

This moment has not produced anything close to the violence of that era. But it is playing out under dystopian circumstances, with a pandemic that has kept much of the nation at home for months, Depression-era job losses and the public bitterly divided on politics and culture.

As governors and mayors urged restraint, President Donald Trump on Saturday urged officials in Minnesota to “get tougher” on the protesters and offered greater military support, a move that would represent a significant escalation in the government’s response to the tensions.

There was a sense of a nation on the brink. “What are you changing by tearing up a city?” Mayor Keisha Lance Bottoms of Atlanta asked protesters there. “You’ve lost all credibility now. This is not how we change America. This is not how we change the world.”

The protests continued with new ferocity even after Derek Chauvin, the former Minneapolis police officer who was shown on a cellphone video kneeling on Floyd’s neck as he lost consciousness, was charged with third-degree murder Friday.

Walz said that the authorities had been overwhelmed by the demonstrations Friday night, which he said had devolved into “absolute chaos.”

The roots of the unrest and division are long and deep.

But the immediate trigger is a protest movement, ignited by the death of Floyd, that reflects the street uprisings of the Black Lives Matter movement that came to prominence six years ago.

The escalating violence and destruction felt like a warning that this moment could be spinning out of control both because of the limitations of a largely spontaneous, leaderless movement and because, protesters and officials warned, there were indications it was also being undermined by agitators trying to sabotage it.

“I need those legitimate folks who are grieving to take this back,” Walz said at an early morning news conference as a bank, a gas station and several other buildings burned. “Why are we talking about anarchists who are burning down damn buildings?”

And, beyond the chaos in Minneapolis, there were widespread fears that a movement protesting police violence and systemic racism was instead being subverted by images of violence and chaos playing out around the country.

In many communities, the protests reflected both Floyd’s death and simmering local controversies.

One hot spot was Louisville, Kentucky. Gunfire broke out in the late hours of a demonstration Thursday that was protesting the shooting death of Breonna Taylor, a 26-year-old emergency medical technician who was killed by Louisville police officers executing a search warrant. Seven demonstrators were injured. It is still unclear who fired the shots, although the authorities said they came from within the crowd.

“We have to be careful to control our message, and violence changes that message,” said Keisha Dorsey, a Louisville city councilwoman who supports police reform. With the endless barrage of news and spin on of social media, she said, it can become easy for a protest to lose all focus. “At that point, that centralized voice, if it’s not cohesive, can get lost,” she said.

A demonstration in Columbus, Ohio, on Thursday night, which ended in clashes between the police and protesters as well as damage to the Ohio Statehouse, was not only about Floyd and Taylor but also about a number of other black people who were killed at the hands of the police, including a 16-year-old killed in a police sting in Columbus in late 2018.

In Phoenix, a local activist called a march which, while not fully supported by the other police accountability groups in the city, ended up drawing hundreds, many of them protesting the long-troubled record of the Phoenix police in addition to the death of Floyd. In Memphis, Tennessee, an aggressive police response to a demonstration organized by local educators Wednesday night prompted a second protest Thursday, in part responding to police actions during the first.

“It started out as the George Floyd issue,” said Ayo Akinmoladun, a Memphis educator who organized what was intended to be a small silent protest. “All of these other issues are now coming out.”

DeRay Mckesson became a well-known activist after spending months in Ferguson, Missouri, chronicling the nightly vigils and clashes with the police over the killing of Michael Brown.

Mckesson is not heading to Minneapolis, where he used to live, to protest. Instead, he has been speaking with organizers on the ground to craft strategy, he said, in line with the work he has done in more recent years to develop policy reforms.

“There needs to be an immediate response to the trauma,” he said, referring to street protests. “There are people who do that, and I support that. I can be most helpful pushing around policy changes, structural changes and helping to make sure the story we tell is consistent with the world we’re trying to build.”

Carol Becker, a longtime Minneapolis resident, took her 13-year-old to witness some of the demonstrations earlier in the week while there was still light out and things were under control. She supported the protests because she believed that the officers were “absolutely wrong,” she said.

But by nightfall, with unrest giving way to tear gas, rubber bullets, and burned and looted businesses, she found herself standing in front of her father’s apartment building, fending off people trying to set it on fire, she said.

“There were protesters at the police precinct,” she said. “When you got even a block away, there weren’t protesters anymore. These people weren’t protesting. They were breaking into things and taking things.”

Still, in city after city, people turned out, most of them hoping for the best.

“I’m here for peace,” said Kenny Washington, 39, of northeast Minneapolis who came out with her newly minted college freshman son, Trenton Washington, 19, after some rest from the exhausting first night of protest. “Destruction is only going to bring chaos. People want to bring change, and we came back to give peace another chance.”

This article was written by John Eligon, Matt Furber and Campbell Robertson, reporters for The New York Times.