A police station in Minneapolis has been set alight during a third night of protests over the death of an unarmed black man in custody on Monday.
A police officer was filmed kneeling on the neck of George Floyd, 46, despite him saying he could not breathe.
President Donald Trump said “thugs” were dishonouring his memory and called on the National Guard to restore order.
Twitter accused Mr Trump of glorifying violence in a post that said: “When the looting starts, the shooting starts.”
Mr Floyd’s family have demanded that the four police officers implicated in his death face murder charges. Prosecutors have said they are still gathering evidence.
The incident has added to longstanding anger over the police killings of black Americans, including the recent case of Breonna Taylor in Kentucky.
There have also been demonstrations in other US cities, including New York, Los Angeles, Chicago, Denver, Phoenix and Memphis.