Widespread demonstrations have taken place, with riot police using tear gas and rubber bullets after their vehicles were set alight in several cities.
President Donald Trump blamed “looters and anarchists” for the violence.
Mr Floyd, a 46-year-old African American, was killed while in police custody in Minneapolis on Monday.
Former policeman Derek Chauvin, 44 and white, has been charged with his murder and is due to appear in court on Monday.
In footage that went viral online, Mr Chauvin can be seen kneeling on Mr Floyd’s neck for several minutes. Mr Floyd repeatedly says that he is unable to breathe.
Large demonstrations have taken place in at least 30 cities across the US.
In Chicago, protesters threw stones at riot officers, who responded by launching tear gas canisters. Several people were arrested on Saturday.
Police in Los Angeles fired rubber bullets as they tried to disperse crowds who threw bottles and set fire to their squad cars. Images later showed people standing on police vehicles that had been damaged.
For the second day running, a large crowd converged on the White House in Washington, DC.
In Atlanta, Georgia, where buildings were vandalised on Friday, a state of emergency was declared for some areas to protect people and property.
Thousands of people also marched through the streets of Minneapolis, New York, Miami, Atlanta and Philadelphia.
Overnight curfews have been now been declared in Minneapolis, Atlanta, Los Angeles, Philadelphia, Portland and Louisville – among other cities.
However, protesters in several cities continue to defy the curfews and widespread looting has been taking place.
In Minnesota, hundreds of troops from the National Guard – a reserve military force that can be called on by the US president or state governors to intervene in domestic emergencies – were brought in late on Friday. (Courtesy BBC)