The man, whose identity is not yet being released, was shot after an incident that began at about 1:25 p.m. Wednesday when officers in a marked police car pulled over a vehicle on Bush Street near Larkin Street.
The man, who was driving the car, got out and fled, and as two officers chased him, he fired at least two shots at them, police said.
The officers were not injured and returned fire, hitting the suspect in the upper torso. He was taken to San Francisco General Hospital, where he was pronounced dead Thursday night, police spokesman Sgt. Daryl Fong said.
While the officers were chasing the suspect, a female passenger in the car slid over to the driver's seat and drove away, police said.
Fong said today that investigators have since located and interviewed the female, and she is no longer considered a person of interest in the case.