Floyd, 46, died Monday night in Minneapolis, with video later showing him on the ground with a police officer's knee pressed against his neck.
“I can't breathe” and “Don’t kill me,” Floyd shouts in the video, which has sparked outrage across the U.S. and led to the firings of four Mineapolis police officers. Protests continuing in Minnesota on Wednesday erupted into violence and looting.
President Trump on Wednesday ordered the FBI and Justice Department to investigate the case.
In Los Angeles, protesters at one point were seen burning an upside-down American flag, FOX 11 of Los Angeles reported.
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Several hundred demonstrators marched in downtown L.A. -- as well as in other cities across the nation -- to show outrage over Floyd's death in police custody. At one point during the march, some of the protesters broke off and entered Highway 101 near Alameda Street, according to the Los Angeles Times.
"When I saw the video of George Floyd getting murdered in cold blood, I've never felt anything like that in my life, man," one of the protesters told Los Angeles's KABC-TV.
Television footage showed some demonstrators halting traffic on 101 and confronting the CHP patrol car -- as the Los Angeles Police Department issued a citywide tactical alert.
Demonstrators captured on video banged on the hood of the cruiser that attempted to move through the crowds and one person appeared to smash the vehicle's rear window with a skateboard, according to the station.
At least one protester was injured and received medical attention after falling off the police vehicle as it drove away, the Los Angeles Times reported.
There were no immediate reports of arrests, but police remained worried over the rise in violence. The freeway has since been cleared.
“I’m concerned. They have exhibited a significant degree of violence,” LAPD Asst Chief Robert Arcos told the paper.
Later, LAPD Chief Michel Moore issued a statement that was posted on Twitter.
"The actions I watched in the video were incredibly disturbing and go against the basic law enforcement principle of preservation of life," Moore wrote. "The lack of compassion, use of excessive force, or going beyond the scope of the law, doesn't just tarnish our badge -- it tears at the very fabric of race relations in this country."
In Memphis, Tenn., police in riot gear used pepper spray against demonstrators, FOX 13 of Memphis reported. Police confirmed making at least two arrests.