Floyd, 46, died after being arrested in Minneapolis, Minnesota, on Monday.
Police deployed tear gas, flash bombs and batons in an effort to disperse angry protesters who defied curfews imposed by at least 25 cities Saturday night, including Chicago, Atlanta, Los Angeles, Louisville, San Francisco and Denver.
The National Guard was also activated in several states, including Texas, Georgia, Washington, Ohio and Kentucky.
A white policeman was arrested on Friday and charged with third-degree murder and manslaughter.
But the arrest did nothing to quell the protests that began peacefully but later turned violent.
In video footage, Derek Chauvin, 44, can be seen pinning 46-year-old Floyd to the ground with a knee on his neck for more than 8 minutes despite repeated pleas from Floyd that he cannot breathe.
The video went viral online, reigniting public anger over police killings of African Americans, and reopening deep wounds over racial inequality across America.
The case follows the high-profile killings by police of Michael Brown in Ferguson, Eric Garner in New York and others that have driven the Black Lives Matter movement.
Chauvin is due to appear in court on Monday. Three other officers present at the time have also since been fired.
President Donald Trump has put the US Army on alert, saying troops could be deployed on the ground very quickly.
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.
The National Guard has been released in Minneapolis to do the job that the Democrat Mayor couldn’t do. Should have been used 2 days ago & there would not have been damage & Police Headquarters would not have been taken over & ruined. Great job by the National Guard. No games!
In Washington DC, a large crowd of protesters clashed with police outside the White House in for the second day running.
Crowd setting an SUV on fire near the White House. Two blocks away. @CBSNews
Some demonstrators managed to overcome the barriers and entree the park in front of the White House, but were driven out by police using shields, batons and pepper spray.
We are a nation in pain, but we must not allow this pain to destroy us. We are a nation enraged, but we cannot allow our rage to consume us. Please stay safe. Please take care of each other.
One of the cities worst affected by the unrest was Los Angeles, where numerous shops have been looted and multiple patrol vehicles were also set on fire.
California Governor Gavin Newsom has declared a state of emergency in the city and activated the National Guard.
At least one person died after being shot in Indianapolis. Police are investigating whether the incident was connected to anti-police protests in the city.
Elsewhere, police officers reacted to the unrest in extraordinary fashion.
Several videos in New York showed a police patrol vehicle driving through crowds of protesters, who were throwing debris at another police car.
Mayor Bill de Blasio called the footage “upsetting” but said it was “inappropriate for protesters to surround a police vehicle and threaten police officers.”