Police say they spotted the man, identified by relatives as Marquis Samson, running west bound on 79th at approximately 5 a.m. Authorities say the officers told the man to stop, but he did not. One officer is said to have run after him while another tried to block him with a car.
According to police, the man allegedly pulled a gun on the officers, who opened fire and killed him.
Fraternal Order of Police spokesman Pat Camden says the officers believed the man was fumbling with something, which police later learned was a black knit cap containing a gun.
Authorities allege the man pulled the gun from the cap.
The man's family disputes the police account of the incident, saying he didn't have a weapon.
The man was pronounced dead on the scene. His identity had not been released later Sunday morning. No other injuries were reported.
The Independent Police Review Authority says it is investigating the shooting.
(The Associated Press contributed to this report.)