Shocking footage has emerged of police officers being run over while in other incidents officers have been shot as unrest spreads in the United States.

A vehicle ploughed through a group of law enforcement officers at a George Floyd demonstration in Buffalo this afternoon (Monday night local time), injuring at least two.

Video posted by a bystander shows a line of police officers, backed up by an armoured personnel carrier, rushing and tackling a man who was being interviewed by a man with a TV camera about 9.30pm. Other officers used batons to whack at protesters, who scattered.

Moments later, there was the sound of firearms discharging off camera, then officers ran as an SUV barrelled through a cluster of officers. At least one appeared to go under the vehicle's wheels.

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The SUV drove around an armoured vehicle and sped off as more gunfire sounded.

The officers were taken to Erie County Medical Centre and authorities said their condition was stable. One is a New York State Police officer who suffered serious but not life-threatening injuries, the agency said. The other is with the Buffalo Police Department.

In St Louis, police say four officers were hit by gunfire after protests that started peacefully Monday became violent overnight, with demonstrators smashing windows and stealing items from businesses and fires burning in the downtown area.

The police department tweeted early Tuesday that the officers were taken to a hospital with injuries that were not believed to be life-threatening.

It was unclear who had fired the shots.

The chaos in St Louis followed continued protests Monday in Missouri over the death of George Floyd and police treatment of African Americans, with gatherings also held in Kansas City and Jefferson City.

On Monday afternoon (US time), several hundred people rallied peacefully outside the justice center in downtown St Louis, including Mayor Lyda Krewson and St Louis Public Safety Director Jimmie Edwards.

Protestors later walked to the Gateway Arch National Park and then onto nearby Interstate 64.

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But later Monday, protesters gathered in front of police headquarters, where officers fired tear gas.

Some protesters smashed windows at a downtown 7-11 store and stole items from inside before the building was set on fire.

Meanwhile, an officer was shot in Las Vegas and authorities are responding to another shooting as people protest the killing of Floyd, authorities said.

The officer was shot in the area of the Las Vegas Strip and an officer was involved in a shooting in the downtown area, according to the Las Vegas Metropolitan Police Department.

The department said both shootings were on Las Vegas Boulevard.

Protesters have been rallying for days across the country over the death of Floyd, who was seen on video pleading that he couldn't breathe with a white police officer pressing his knee into his neck for several minutes before Floyd stopped moving.

- AP