Curfews have been imposed in nearly 40 cities, but people have largely ignored them, leading to tense stand-offs.
Riot police clashed with protesters in New York, Chicago, Philadelphia and Los Angeles, firing tear gas and pepper bullets to try to disperse the crowds.
Police vehicles were set on fire and shops were looted in several cities.
The National Guard – the US reserve military force for domestic emergencies – said on Sunday that 5,000 of its personnel had been activated in 15 states and Washington, DC, where crowds once again gathered near the White House, this time lighting fires and throwing stones at riot officers.
“State and local law enforcement agencies remain responsible for security,” the National Guard added.
Police in Washington DC have fired tear gas at demonstrators who set fire to properties near the White House. They include a historic church, St John’s Episcopal Church, known as the church of the presidents, near the White House.
It has emerged that in Friday night’s unrest, President Donald Trump was briefly taken by the secret service into an underground bunker at the White House, for his safety.
he US is witnessing the most widespread racial turbulence and civil unrest since the violent backlash to the assassination of Martin Luther King in 1968, says the BBC’s Nick Bryant.
More than 75 cities have seen protests, with streets only days ago deserted because of coronavirus, thronged with demonstrators marching shoulder to shoulder.
The Floyd case has reignited anger over police killings of black Americans. For many, the outrage also reflects years of frustration over socio-economic inequality and segregation, not least in Minneapolis itself, where George Floyd died.