Hundreds of people rallied outside the White House, which was briefly put under lockdown on Friday, demanding justice over the death of George Floyd.
Minnesota, New York, Atlanta and other regions have seen violent unrest.
A former Minneapolis police officer has been arrested and charged with murder over Mr Floyd’s death in custody.
Derek Chauvin, who is white, was shown in footage kneeling on 46-year-old Mr Floyd’s neck on Monday. He and three other officers have since been sacked.
Mr Chauvin, 44, is due to appear in court in Minneapolis for the first time on Monday.
President Donald Trump has described the incident as “a terrible, terrible thing” and said he had spoken with Mr Floyd’s family, whom he described as “terrific people”.
Minnesota remains the most volatile region, with curfews ordered for the Twin Cities of Minneapolis-Saint Paul from 20:00 to 06:00 on Friday and Saturday evening.
Protesters defied the curfew on Friday. Fires, many from burning cars, were visible in a number of areas with fire officials unable to reach some sites.
Television pictures also showed looting in Minneapolis, with police officers thin on the ground.
On Friday evening, crowds gathered near the White House in Washington waving photographs of Mr Floyd and chanting “I can’t breathe” – invoking his last words and those of Eric Garner, a black man who died after being held in a police chokehold in New York in 2014.
The White House was then temporarily placed on lockdown, with the US Secret Service closing entrances and exits.
In Atlanta, a state of emergency was declared for some areas to protect people and property. Buildings were vandalised and a police vehicle was set alight as protesters gathered near the offices of news broadcaster CNN.
Mayor Keisha Lance Bottoms issued a passionate plea, saying: “This is not a protest. This is not in the spirit of Martin Luther King Jr. You are disgracing our city. You are disgracing the life of George Floyd.”
In New York’s Brooklyn district, protesters clashed with police, throwing projectiles, starting fires and destroying police vehicles. A number of officers were injured and many arrests made.
Mayor Bill de Blasio tweeted: “We don’t ever want to see another night like this.”
In Dallas, officers launched tear gas canisters after they were pelted with stones.
Protesters blocked roads in Los Angeles and also in Oakland, where windows were smashed and “Kill Cops” graffiti sprayed.
Mr Chauvin has been charged with third-degree murder and second-degree manslaughter over his role in Mr Floyd’s death.
Mr Floyd’s family and their lawyer, Benjamin Crump, said that this was “welcome but overdue”.
The family said they wanted a more serious, first-degree murder charge as well as the arrest of the three other officers involved.
Hennepin County Prosecutor Mike Freeman said he “anticipates charges” for the other officers but would not offer more details.
Mr Freeman said his office “charged this case as quickly as evidence has been presented to us”.
“This is by far the fastest that we’ve ever charged a police officer,” he noted.
According to the criminal complaint, Mr Chauvin acted with “a depraved mind, without regard for human life”.
The full report by the county medical examiner has not been released, but the complaint states that the post-mortem examination did not find evidence of “traumatic asphyxia or strangulation”.
The medical examiner noted Mr Floyd had underlying heart conditions and the combination of these, “potential intoxicants in his system” and being restrained by the officers “likely contributed to his death”.
