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.
Only at about midnight (05:00 GMT) did police and National Guard troops move in in any numbers, the Star Tribune reports.
State Governor Tim Walz, in an early morning press briefing, described the situation as "chaotic, dangerous and unprecedented".
He said he took responsibility for "underestimating the wanton destruction and the sheer size of this crowd" when questioned about the lack of police on the streets.
He said the Guard deployment was the largest in state history but admitted "there's simply more of them than us". He said those on the streets "don't give one damn" about the stay-at-home order.
The Pentagon has put the military on alert for possible deployment in Minneapolis.
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.
[...]
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
Detroit, police are investigating after a 19-year-old man was killed when a vehicle pulled up to protesters and shots were fired into the crowd.
In
Dallas, officers launched tear gas canisters after they were pelted with stones, with tear gas also fired in
Phoenix.
Police in
Portland, Oregon, declared a riot, with reports of looting and a number of fires.
Protesters blocked roads in
Los Angeles and also in
Oakland, where windows were smashed and "Kill Cops" graffiti sprayed.
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