Clayton County police Officer Sean Callahan, 24, died of his injuries around 5:16 a.m. Tuesday, police said.
The shooting happened Monday afternoon after police were called to a domestic dispute near a motel on Davidson Parkway in Stockbridge — about 20 miles southeast of Atlanta.
Police had been called to a domestic dispute around 2 p.m. Monday. Officers tried to arrest a couple at the motel, but the man broke free. Officers chased after the man, who fired shots at them, Clayton County Police Chief Gregory Porter told reporters. Police returned fire and killed him.
The unidentified woman who was involved in the dispute was taken into custody.
Callahan was taken to Grady Memorial Hospital in Atlanta, where he had been in critical condition Monday night.
"Our job as police officers is to protect and serve. Our job requires us to run to face the danger, no matter what the circumstances," Lt. Chris Windley said in Tuesday's statement.
Callahan is the second Clayton County police officer to be seriously hurt while on duty within a week.
On Wednesday, one of two burglary suspects hit officer Michael Hooks with a truck in Jonesboro and fled the scene. Authorities arrested one suspect and are still searching for the 36-year-old man who hit Hooks.