A woman who died in a weekend hostage standoff at a Trader Joe's store in Los Angeles was killed by a bullet fired by a police officer, the city's police chief said on Tuesday.

The woman, who was identified as Melyda Corado, a manager at the store, by relatives, was one of several people who had run out of the market when a shooting suspect, Gene Atkins, 28, crashed his car outside the store on Saturday while being chased by police, Los Angeles Police Chief Michel Moore told reporters.

"I'm sorry to report that we've now determined through our forensic investigation that one of the officers' rounds struck Ms. Corado as she was exiting the market and was in close proximity to Atkins," Moore said.

After being struck, Corado ran back into the store and collapsed behind the manager's desk.

Atkins is being held on a bail of $9 million and is scheduled to appear in court on Monday, Moore said. He had initially been held on $2 million bail.

Atkins is suspected of repeatedly shooting his grandmother in a separate part of the city before taking a girl hostage in a car, being chased by police and crashing outside the Trader Joe's. He exchanged gunfire with police, threatened to kill hostages and suffered an arm wound before surrendering.

Atkins' grandmother and the girl, who media identified as his girlfriend and who Atkins allegedly shot in the head, remained in critical condition, Moore said.

People inside the market carried Corado out of the building and she was treated by members of the Los Angeles Fire Department but died of the gunshot wounds.

The first two officers on the scene, who have not been identified, had been members of the Los Angeles police department for two and six years respectively, Moore said.

The incident began when Atkins got into an argument with his grandmother and the 17-year-old girl. He allegedly shot his grandmother multiple times before fleeing with the 17-year-old and ending up at the Trader Joe's, where 30 people were inside, Moore said.