It happened just before 7 p.m. in the 7300 block of Pickering Avenue.
According to the Los Angeles County Sheriff's Department, officers were observing the suspect, 25-year-old Edgar Gonzalez, who was identified as the alleged shooter involved in a murder in Santa Fe Springs on July 30.
When officers initiated a traffic stop, Gonzalez allegedly got out of his car and ran away from officers, authorities said.
Officers went after Gonzalez, and that's when the shooting occurred.
Officials said Gonzalez discarded a semi-automatic handgun and then continued trying to run away west on Mar Vista Avenue. He eventually surrendered and was taken into custody.
The police officer suffered two non-life-threatening gunshot wounds to his lower body, while Gonzalez was shot in the hand, according to authorities.
Both the officer and Gonzalez were taken to the hospital where both remain in stable condition.
"Last night's shooting incident, a running gun battle with a violent suspect, exemplifies the courage and determination of our law enforcement officers, who take on the daily mission of keeping our communities safe, while putting their personal safety in great jeopardy," Chief Aviv Bar said in a statement to FOX 11.
"The environment in which these selfless men and women operate is becoming ever so more dangerous in Los Angeles County. Too many career criminals and violent repeat offenders are on the streets receiving break after break and reprieve after reprieve from the criminal justice system, while continuing to victimize others, including taking violent action against our law enforcement officers. Please keep our men and women in your thoughts and prayers. They are amazing people who truly care about the safety and security of our community."
Anyone with information about this incident is encouraged to contact the Los Angeles County Sheriff's Department's Homicide Bureau at (323) 890-5500.