The latest unrest on Thursday in Minnesota's largest city went largely unchecked, despite Governor Tim Walz ordering in the National Guard after the first two days of disturbances sparked by Monday night's fatal arrest of Floyd.

But some civil rights advocates say wider police denunciations are empty words without meaningful reform behind them.

A bystander's disturbing video shows white officer Derek Chauvin kneeling on Floyd's neck, even as he begs for air and slowly stops talking and moving.

"There is no need to see more video," Chattanooga, Tennessee, police chief David Roddy tweeted on Wednesday. "There no need to wait to see how 'it plays out'. There is no need to put a knee on someone's neck for NINE minutes. There IS a need to DO something. If you wear a badge and you don't have an issue with this ... turn it in."

Sheriffs and police chiefs have strongly criticised the four Minneapolis officers on social media and praised the city's chief for his quick dismissal of them. Some called for them to be criminally charged.

"I am deeply disturbed by the video of Mr. Floyd being murdered in the street with other officers there letting it go on," Polk County, Georgia, sheriff Johnny Moats wrote on Facebook. "I can assure everyone, me or any of my deputies will never treat anyone like that as long as I'm Sheriff. This kind of brutality is terrible and it needs to stop. All Officers involved need to be arrested and charged immediately."

"Not going hide behind 'not being there,'" tweeted San Jose Police, California, chief Eddie Garcia. "What I saw happen to George Floyd disturbed me and is not consistent with the goal of our mission. The act of one, impacts us all."

But Gloria Browne-Marshall, a civil rights attorney, said she wouldn't be a "cheerleader" for a handful of chiefs who harshly decried the officers' behaviour.

"Any minute progress is seen as miraculous because so little has been done for so long," she said. "It's nothing close to progress or what outrage would be taking place if it was a white man as the victim."

Melina Abdullah, co-founder of Black Lives Matter in Los Angeles, said the three other officers who did not intervene to stop the "lynching" contributed to a long-standing police racism and oppression.

"We've got to remember that it was not just officer Chauvin who was sitting on George Floyd's neck.

The Los Angeles and Chicago departments - both rocked before by police brutality scandals - addressed Floyd's death and its potential effect on race relations.

Even New York police weighed in. Eric Garner died in the city in 2014 after he was placed in a chokehold by police and uttered the same words Floyd did: "I can't breathe".

City officials took five years to fire the officer, and no criminal or federal charges were brought.

"What we saw in Minnesota was deeply disturbing. It was wrong," NYPD Commissioner Dermot Shea wrote. "We must take a stand and address it. We must come together, condemn these actions and reinforce who we are as members of the NYPD. This is not acceptable ANYWHERE."

Harris County, Texas, sheriff Ed Gonzalez said: "We keep thinking that the last one will be the last one, and then another one surfaces."

Australian Associated Press