Demonstrators clashed with police and set a store alight during a second night of protests in the US city of Minneapolis Wednesday over the killing of a black man by an officer who held him to the ground with a knee on his neck.

Police fired tear gas and formed a human barricade to keep protesters from climbing a fence surrounding the Third Precinct, where the officers accused of killing George Floyd worked before they were fired on Tuesday.

They pushed protesters back as the crowd grew, a day after firing rubber bullets and more tear gas on thousands of demonstrators angered by the latest death of an African-American at the hands of US law enforcement.

Outrage has grown across the country at Floyd's death Monday, fuelled in part by bystander cellphone video which shows him, handcuffed and in the custody of four white police officers, on the ground while one presses his knee into the victim's neck.

President Donald Trump in a tweet called Floyd's death "sad and tragic", and all four officers have been fired, as prosecutors said they had called in the FBI to help investigate the case, which could involve a federal felony civil rights violation.

Minneapolis police chief Medaria Arradondo cautioned protestors Wednesday to remain peaceful.

But by 10:00 pm (0300 GMT Thursday) an auto parts store across from the precinct had been set alight and a nearby Target was being looted, according to US media.

Police continued to hold the crowds back from scaling a fence into the precinct's parking lot, where their cruisers contain guns.

Protesters remained peaceful at two other locations in the city.

At the place where Floyd was first taken into custody by the officers people chanted and barbecued, carried placards and spoke out. Bouquets were set out as tributes to Floyd, and there was no vandalism.

Calls for justice came from around the country.

"I would like those officers to be charged with murder, because that's exactly what they did," Bridgett Floyd, the victim's sister, said on NBC television.

"They murdered my brother.... They should be in jail for murder."

Minneapolis mayor Jacob Frey said he could not understand why the officer who held his knee to Floyd's neck on a Minneapolis street until the 46-year-old restaurant worker went limp has not been arrested.

"Why is the man who killed George Floyd not in jail? If you had done it, or I had done it, we would be behind bars right now," Frey said.

"Based on what I saw, the officer who had his knee on the neck of George Floyd should be charged," he said.