Demonstrators smashed windows and looted stores in New York City late on Monday and set fire to a Los Angeles strip mall amid widespread protests over the killing of an African-American man in police custody.

Four officers were shot and wounded in St Louis, Missouri, and one in Las Vegas was critically wounded, authorities said on Tuesday.

Trump has threatened to use the military to battle the violence that has erupted often at night after a day of peaceful protests joined by a cross-section of Americans.

He has derided local authorities, including state governors, for their response to the disturbances.

“NYC, CALL UP THE NATIONAL GUARD. The lowlifes and losers are ripping you apart. Act fast!” Trump tweeted on Tuesday.

New York Governor Andrew Cuomo voiced outrage at the chaos in America’s largest city, saying its mayor and police force “did not do their job last night”.

He said he believed Mayor Bill de Blasio underestimated the scope of the problem.

Cuomo said he had offered mayors support from state police or 13,000 National Guard who are on stand-by and said that with a 38,000-strong police force, New York City should be able to address its unrest on its own.

De Blasio poured cold water on the idea of bringing the National Guard to America’s largest city.

Meanwhile, the owner of a popular barbecue spot who was fatally shot by police in Louisville, Kentucky, had fired a gun as officers approached, the city’s acting police chief said.

Acting Police Chief Robert Schroeder said security camera footage showed David McAtee opening fire while officers were trying to clear a crowd from a car park on Monday.

Schroeder said police were releasing the video to provide transparency.

“It does not answer every question, including why did he fire and where were police at the time he fired?” he said on Tuesday.

The Louisville police chief was fired after it was revealed officers involved in McAtee’s shooting had failed to activate their body cameras.

In St Louis, four officers were recovering after being shot overnight amid clashes between police and crowds throwing rocks and other projectiles.

And a police officer was shot during protests in Las Vegas, police there said in a statement.

Officers were injured in clashes elsewhere, including one who was in critical condition after being hit by a car in the Bronx.

In Atlanta, six officers will face charges for an incident in which two college students were removed from their car and tasered, Fulton County District Attorney Paul Howard told a briefing.

Two of the six officers were let go on Sunday.

And a police officer in Sarasota, Florida, was placed on leave on Tuesday after video surfaced showing the officer kneeling on a man’s back and neck during an arrest in May.

The violent US protests were triggered by the death of George Floyd, a 46-year-old African-American who died after a white policeman pinned his neck under a knee for nearly nine minutes in Minneapolis on May 25.

Minneapolis police officer Derek Chauvin, 44, has been charged with third-degree murder and second-degree manslaughter.

Three other officers involved have not been charged.

-AAP