Images on local media showed hundreds of protesters in the streets on Saturday and flames engulfing the Wendy's restaurant where 27-year-old Rayshard Brooks was killed.
The officer who shot Brooks was dismissed on Saturday and identified by Atlanta police as Garrett Rolfe. The second officer was placed on administrative duty, according to ABC News.
Mayor Keisha Lance Bottoms - who has been touted as a potential running mate for Democratic presidential candidate Joe Biden - earlier announced the resignation of Chief Erika Shields.
Wendy's employees called police on Friday night to complain that Brooks was asleep in his car and blocking other customers on the premises, an official report said.
He failed a sobriety test and resisted when police tried to arrest him, the Georgia Bureau of Investigation (GBI) said.
Surveillance video showed "that during a physical struggle with officers, Brooks obtained one of the officer's Tasers and began to flee from the scene," the report continued.
"Officers pursued Brooks on foot and during the chase, Brooks turned and pointed the Taser at the officer. The officer fired his weapon, striking Brooks," it said.
Brooks was taken to hospital but died after surgery, it said, adding that one officer was injured.
An attorney acting for the dead man's family said disproportionate force was used in the confrontation.
"In Georgia a Taser is not a deadly weapon - that's the law," L. Chris Stewart told reporters.
"Support came, in I think 2 minutes. He would have been boxed in and trapped. Why did you have to kill him?"
"(The officer) had other options than shooting a man in the back."
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Brooks has four children, Stewart added, and had celebrated the birthday of his eight-year-old girl earlier on Friday.
His death is the 48th shooting involving an officer the GBI has been asked to investigate this year, according to local newspaper the Atlanta Journal-Constitution. Fifteen of those incidents were fatal.
The unrest comes as the US faces a historic reckoning on systemic racism, with mass civil unrest ignited by the May 25 killing of another African-American man, George Floyd, while in police custody.
Floyd died after a white Minneapolis police officer knelt on his neck for nearly nine minutes.
Protests which spread first around the country then the globe, have forced a conversation on the legacies of slavery, colonialism and white violence against people of color, as well as the militarization of police in America.
Police chief Shields had worked for Atlanta's police department for more than two decades.
"Because of her desire that Atlanta be a model of what meaningful reform should look like across this country, Chief Shields has offered to immediately step aside as police chief," the mayor said in televised comments.
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