Witnesses say the officer kept his knee there for seven minutes - even after Floyd said repeatedly he couldn't breathe.
RELATED: Officer who put knee on man's neck should be charged, Minneapolis mayor says
San Jose Police Chief Eddie Garcia has studied the video.
"I think I thought what every good, hard-working police officer quite frankly thinks - was appalled" he said.
Garcia took to Twitter to make his feelings known
The tweet says in part "what I saw happen to George Floyd disturbed me and is not consistent with the goal of our mission."
He told ABC-7 News, "As leaders in law enforcement when we see something we know in our hearts is wrong we can't remain silent."
In Minneapolis, protests over the death of a black man in a confrontation with white officers have escalated over several nights, with demonstrators breaking windows and setting fires and police firing rubber bullets to disperse them.
"The video is extremely disturbing. I can't put it any other way" according to San Francisco Police Chief Bill Scott.
RELATED: George Floyd's sister wants justice after brother dies in police custody
He says police departments work hard to gain and maintain the trust of their communities, and this does not help. He's looking at the incident through the eyes of a chief who is also African American.
"Some of it is personal to me in terms of being an African American man in leadership in policing. I think people do look at us, at people like me in these position to make a difference" Scott said.
Oakland's interim police chief Susan Manheimer denounced the treatment of Floyd as police brutality in a statement that says in part, "We stand with all in our community who have traditionally been marginalized, oppressed and who have been harmed by our systems and institutions."
RELATED STORIES & VIDEOS:
- Who was George Floyd? Former Houston high school football star started new life in Minneapolis
- George Floyd death: Officer who put knee on man's neck should be charged, Minneapolis mayor says
- Violent protests rock Minneapolis for 2nd straight night over in-custody death
- Minneapolis mayor: Officer who put knee on George Floyd's neck should be charged
- 'Firing them is not enough' | George Floyd's sister wants justice after brother dies in police custody
- False news swirls around Officer Derek Chauvin after George Floyd's death
- 'Firing them is not enough' | George Floyd's sister wants justice after brother dies in police custody
- Rubber bullets, chemical irritant deployed as thousands march to protest George Floyd's death
- 4 officers fired after video shows Minneapolis police officer kneeling on neck of black man who died