Tens of thousands of people marched in Washington DC, in the city's largest protest so far. Security forces blocked any approach to the White House.
Crowds also demonstrated in New York, Chicago, LA and San Francisco.
Meanwhile, people paid their respects to Mr Floyd in North Carolina, where he was born, before a memorial service.
Mr Floyd, an unarmed black man, died in police custody in Minneapolis on 25 May. Video showed a white police officer kneeling on his neck for almost nine minutes while he is pinned to the floor.