The show of force in Minneapolis came after three days when police largely avoided engaging protesters, and after the state poured in more than 4,000 National Guard troops to the city and said the number would soon rise to almost 11,000.
Protests spread around the globe, with events in London and Berlin on Sunday and others on Monday including in New Zealand, Australia and the Netherlands.
Curfews have been ordered in more than two dozen cities to try and stem the violence, while the National Guard have also been deployed across several states.
President Donald Trump has condemned the killing of Floyd and promised justice, but has also described the current protesters as "thugs".More news: Greece to resume flights from United Kingdom on 15 June with strict rules
National Guard units also were mobilized by the governors of Ohio, Missouri, Wisconsin and Tennessee.
Photographer Evan Hreha told Storyful that people who had seen the incident claimed that a Seattle police officer had sprayed the child with mace.
Four nights of arson, looting and vandalism in parts of Minneapolis and St Paul prompted the activation of the full Minnesota National Guard for the first time since the Second World War.
Two members of a Reuters TV crew were hit by rubber bullets and injured in Minneapolis on Saturday night when police moved into an area occupied by about 500 protestors in the southwest of the city shortly after the 8 pm curfew.
Floyd was suspected of passing a counterfeit bill at a Minneapolis convenience store.More news: Nick Saban Releases Powerful Statement Following George Floyd's Murder
Video from the arrest shows a police officer kneeling on Mr Floyd's neck for several minutes before his death.
The officer, Derek Chauvin, has been fired and charged with murder.
The anger on the streets has been widespread. Another state TV message accused USA police agencies in Washington of "setting fire to cars and attacking protesters", without offering any evidence.
The demonstrations brought out a diversity of people.
De Blasio said he had not seen a separate video showing an officer pulling down the mask of a black protester to spray something in his face.More news: No new cases reported
His death caused outrage across a nation that is politically and racially divided during a polarizing presidential campaign, reigniting protests that have flared repeatedly in recent years over police killings of black Americans.