The chase began around noon when officers spotted a stolen Saab and tried to pull it over, Officer Albie Esparza said.
The driver refused to yield and led officers on a brief pursuit, but police called off the chase because it was getting too dangerous, Esparza said.
A short time later, police learned of a collision that had occurred at 19th and Third streets in the city's Dogpatch neighborhood, where the driver of the Saab had tried to squeeze through two cars and gotten jammed, according to Esparza.
When police arrived, one officer drove toward the Saab trying to block the driver in, and at that point the suspect attempted to ram the officer's car, Esparza said.
Esparza said that the officer felt threatened and fired multiple rounds at the suspect. It is not clear whether the suspect was hit by the gunfire, but he was able to accelerate away, police said.
One person in another car suffered minor injuries in the Dogpatch collision and was treated at the scene, Esparza said. No officers were hurt, he said.
Police soon found the Saab abandoned near 25th and Dakota streets and determined that the suspect had fled on foot, Esparza said.
Officers have set up a perimeter around the public housing complex there and are conducting a unit-by-unit search, police said.
Police are advising people to avoid the area.