MINNEAPOLIS, May 29 — Peaceful rallies gave way to a third night of arson, looting and vandalism in Minneapolis yesterday as protesters vented their rage over the death of a black man seen on video gasping for breath while a white police officer knelt on his neck.

The latest spasm of unrest in Minnesota's largest city went largely unchecked, despite Governor Tim Walz ordering the National Guard activated to help restore order following the first two days of disturbances sparked by Monday night's fatal arrest of George Floyd, 46.

In contrast with Wednesday night, when rock-throwing demonstrators clashed repeatedly with police in riot gear, law enforcement kept a low profile around the epicentre of the unrest, outside the city's Third Precinct police station.

Protesters massing outside the building briefly retreated under volleys of police tear gas and rubber bullets fired at them from the roof, only to reassemble and eventually attack the building head on, setting fire to the structure as police seemed to withdraw. Protesters were later observed on the roof.

A car and at least two other buildings in the vicinity were also set ablaze, and looters returned for a second night to a nearby Target discount store, left boarded up and vacant from the previous night, to make off with whatever remained inside.

Fire officials said 16 buildings were torched on Wednesday night.

There was no immediate sign of National Guard troops at the police station or at a peaceful daytime rally and march around the Hennepin County Government Center in downtown Minneapolis.

Local, state and federal law enforcement officials sought earlier in the day to ease racial tensions sparked by Floyd's death by vowing to achieve justice.

Four city police officers involved in the incident, including the one shown pressing his knee into Floyd's neck as he lay on the ground, moaning, "please, I can't breathe," were fired from their jobs the next day.

The Floyd case was reminiscent of the 2014 killing of Eric Garner, an unarmed black man in New York City who died after being put in a banned police chokehold as he, too, was heard to mutter, “I can't breathe.”

Garner's dying words became a rallying cry for the Black Lives Matter movement that formed amid a wave of killings of African-Americans by police.

Throughout the day, protesters pressed their demands that the four policemen be arrested and prosecuted.

“There is probable cause right now” to make those arrests, civil rights activist the Rev. Al Sharpton said as he addressed the crowd. “We're not asking for a favor. We're asking for what is right.”

Garner's mother, Gwen Carr, said Floyd's case was like “opening up an old wound, and pouring salt into it.”

At a morning news briefing, Police Chief Medaria Arradondo publicly apologised to Floyd's family, conceding his department had contributed to a "deficit of hope" in Minneapolis.

'Give us time to do this right?

Hours later, officials overseeing investigations from the US Justice Department, FBI, Minnesota Bureau of Criminal Apprehension and local prosecutors appealed for calm at a joint news conference, as they gathered evidence.

“Give us the time to do this right, and we will bring you justice,” County Attorney Mike Freeman told reporters. He acknowledged the policeman's conduct depicted in the video was “horrible,” but said, “My job is to prove that he has violated a criminal statute.”

Minnesota's US attorney, Erica McDonald, pledged a “robust and meticulous investigation into the circumstances surrounding” Floyd's arrest and death.

The federal investigation, which Attorney General William Barr had designated a “top priority,” will focus on whether the arresting officers used the “colour of law” to deprive Floyd of his civil rights, a crime under US law, she said.

Floyd, a Houston native known affectionately to friends as “Big Floyd” and who had worked as a nightclub security staffer, was reportedly suspected of trying to pass counterfeit money when police took him into custody.

Wednesday's disturbances, punctuated by looting, vandalism and arson, began hours after Mayor Jacob Frey urged local prosecutors to file criminal charges in the case.

Most protesters had been peaceful, while a smaller, core contingent engaged in unruly behaviour, the police chief said.

Sympathy protests erupted on Wednesday in Los Angeles and yesterday in Denver, with hundreds of demonstrators blocking freeway traffic in both cities.

In a sign the Floyd case had garnered international attention, the United Nations High Commissioner for Human Rights Michelle Bachelet urged US authorities yesterday to deal with “entrenched and pervasive racial discrimination” in America's criminal justice system.

The city named the four officers involved in the encounter as Derek Chauvin, Thomas Lane, Tou Thao and J Alexander Kueng. Local news media have identified Chauvin as the officer seen kneeling on Floyd's neck.

Chauvin's attorney, Tom Kelly, declined comment in an email to Reuters.

Police department records posted online show 18 internal affairs complaints filed against Chauvin, 16 of which were closed without discipline. — Reuters