The incident was reported shortly after 5 am near Main and E. 17th streets, just off the 10 Freeway, according to the Los Angeles Fire Department.
According to the Los Angeles Police Department, the pursuit began when officers saw a gun being thrown out of a green minivan near Central Avenue and the 10 Freeway. That gun has since been recovered, authorities added.
Officers chased the vehicle for about two minutes before the collision.
Firefighters had to free one person who became trapped in the van as a result. One passenger in the suspect vehicle died at the scene.
Three other individuals were taken to the hospital, where another passenger of the minivan died. The driver and a third occupant sustained non-life threatening injuries.
Meanwhile, the bus driver, the only person aboard the bus, declined medical treatment.
Additional details about the crash were not released.