Four US police officers were shot and wounded in the Midwestern city of St Louis, Missouri, during protests over the killing of George Floyd which turned violent, police said early Tuesday.

Their injuries were "non-life threatening," city police chief Colonel John Hayden said. Two were shot in the leg, one in the foot and one in the arm, Hayden told reporters as he said police were struggling to bring the city under control after a night of looting and vandalism.

Following a peaceful protest Monday afternoon, Hayden said a couple of hundred later started looting and throwing rocks and fireworks at police, who responded with "munitions."

"Mr Floyd was killed somewhere else and they're tearing up cities all across the country," he said. "We're still out trying to get control," with the help of the National Guard, he said.

Thousands of people have participated in nationwide demonstrations against police brutality and racism since Floyd's killing a week ago. Many of them have been peaceful but others have seen clashes between protestors and police and destruction of property.

"I don't think anyone understands why this mayhem is going on across the country," a visibly emotional and frustrated Hayden said. He said the four wounded officers were standing by a police line when they were hit by gunfire.

"Some coward fired shots at officers and now we have four in the hospital, but thank God they're alive," Hayden said. "Can we make some sense out of this?"

He said it was not clear if more than one shooter was involved and no arrests had been made so far. "As we speak we're trying to get control of the city, still hearing gunfire and everything," he said. "This is horrible."

The violence in St Louis came as a police officer was shot in Las Vegas, Nevada, reports said. ABC-affiliate KTNV said the shooting occurred late Monday night near a casino on the Las Vegas Boulevard. It was not clear if it was related to protests over the killing of Floyd.

Police were also involved in a separate shooting in downtown Las Vegas, KTNV said. "My Office has been notified that the Las Vegas Metropolitan Police Department is currently working two separate incidents in Las Vegas," Nevada governor Steve Sisolak tweeted.