In Buffalo, New York State, two officers were suspended after they were seen shoving an elderly white man to the ground.
And in New York City, police were captured on video roughly handling demonstrators as they ran away.
The reports come hours after a memorial for Floyd in Minneapolis, the city where he died at the hands of police.
His killing, also captured on video, has caused outrage and sparked a wave of protests against racial discrimination and police treatment of African Americans in cities across the US and the world.
The vast majority of demonstrations over the past eight days have been peaceful but some have descended into violence and rioting, with curfews imposed in a number of cities.
At one protest, security forces in Washington DC fired pepper balls and smoke bombs to disperse demonstrators outside the White House, allowing President Donald Trump to walk to a nearby church for a photo opportunity.
In response to this on Thursday, civil rights group the America Civil Liberties Union filed a lawsuit, accusing the president, the attorney general and others of violating the constitutional rights of protesters.
“When the nation’s top law enforcement officer becomes complicit in the tactics of an autocrat, it chills protected speech for all of us,” said ACLU official Scott Michelman, quoted by Reuters.
In a separate development, police in Arizona released details of the killing of another African American, Dion Johnson, in Phoenix on 25 May, the same day as Floyd.
Johnson was shot dead by state troopers after being found “passed out in the driver’s seat” of a car which was partially blocking traffic, a police statement said.
“During the trooper’s contact with the suspect, there was a struggle and the trooper fired his service weapon striking the suspect,” police said.
The statement was only released after Johnson’s family was offered audio of the police dispatch and transportation department video of the incident. (Courtesy BBC)