Shortly before noon, officers in East Oakland spotted a car that had been reported stolen out of West Oakland and tried to pull it over, police said.
The driver refused to yield and led police on a short chase before the car's occupants got out and fled on foot near 86th and Bancroft Avenues, police said.
At some point, police fired at one suspect, but it appears no one was injured, police said.
Police Sgt. Chris Bolton said at least one suspect brandished a gun and may have fired at officers. One suspect may be in custody, and police are searching the neighborhood for additional suspects, he said.
They have shut down streets between 88th and 84th Avenues, from Bancroft Avenue to Olive Street.
Castlemont High School and East Oakland Pride Elementary School were both placed on lockdown throughout the afternoon but students were released at 3:30 p.m.
Bolton said police are advising people to avoid the area and are asking residents in that neighborhood to report any suspicious activity.