Pleading through tears, the family of a black man killed by Atlanta police outside a drive-thru demanded changes in the criminal justice system and called on protesters to refrain from violence amid heightened tensions across the US three weeks after George Floyd's death in Minneapolis.

An autopsy found that 27 year-old Rayshard Brooks was shot twice in the back late on Friday by a white officer who was trying to arrest him at a fast food restaurant for being intoxicated behind the wheel of his car. Brooks tried to flee after wrestling with officers and grabbing a stun gun from one of them.

"Not only are we hurt, we are angry,” said Chassidy Evans, Brooks’ niece. “When does it stop? We’re not only pleading for justice. We’re pleading for change.”

About 20 of Brooks’ children, siblings, cousins and other family members sobbed at a news conference as more than 1,000 people gathered not far away at an NAACP-led protest outside the Georgia Capitol.

Floyd's death on May 25 after a white Minneapolis officer pressed his knee into the black man's neck sparked demonstrations and scattered violence across the US, and Brooks' killing rekindled those protests in Atlanta. The Wendy’s restaurant where Brooks was shot was burned down over the weekend.

Evans said there was no reason for her uncle ‘to be shot and killed like trash in the street for falling asleep in a drive-thru’.

"Rayshard has a family who loves him who would have gladly come and got him so he would be here with us today,” she said.

Relatives described Brooks as a loving father of three daughters and a stepson who had a bright smile and a big heart and loved to dance. His oldest daughter learned her father was killed while celebrating her eighth birthday with cupcakes and friends, wearing a special dress as she waited for Brooks to take her skating, said Justin Miller, an attorney for the family.

“There’s no justice that can ever make me feel happy about what's been done," said Tomika Miller, Brooks' widow. "I can never get my husband back. ... I can never tell my daughter he’s coming to take you skating or for swimming lessons.”

She asked those demonstrating to ‘keep the protesting peaceful’, saying: “We want to keep his name positive and great.”

Officer Garrett Rolfe, who fired the shots that killed Brooks, was fired, and the other officer at the scene, Devin Brosnan, was put on desk duty. Police Chief Erika Shields resigned a day after the shooting.

Fulton County District Attorney Paul Howard said he hopes to decide by midweek whether to charge the officers. The Georgia Bureau of Investigation was took over the investigation.

Police had been called to the fast food restaurant because of complaints that a car was blocking the drive-thru lane. An officer found Brooks asleep in the car.

Police video showed Brooks cooperating with the officers for more than 40 minutes until a breath test determined his blood-alcohol level was over the legal limit. When one of the officers moved to handcuff him, Brooks tried to run and the officers took him to the ground.

Brooks broke free and took off with a stun gun but was shot. Rolfe told authorities that Brooks had fired the stun gun at him.

Asked why Brooks ran, family attorney L. Chris Stewart suggested that he may have feared for his life.

"They put George Floyd in handcuffs and he was subsequently killed,” Stewart said. “So just getting put in handcuffs if you’re African American doesn’t mean, oh, you’re going to get nicely taken to the back of a police car.”