The suspect's car crashed next to the store and he opened fire on the officers chasing him, before entering the premises as shoppers ran for cover, the Los Angeles Times said.
The suspect has been shot.
A woman was shot and killed when the gunman ran into a busy Los Angeles supermarket where he held dozens of people hostage for about three hours Saturday before handcuffing himself and surrendering to police.
About two hours before taking the hostages, police say the man shot his grandmother seven times and wounded another woman, who he forced into a car. Police chased the vehicle and exchanged gunfire with the man, who crashed into a pole outside the Trader Joe's in the city's Silver Lake section and ran into the store.
Frightened customers and workers dove for cover as police bullets fired at the suspect shattered the store's glass doors. Some inside the supermarket climbed out windows as scores of police and firefighters and 18 ambulances converged on the scene and prepared for mass casualties.
Prior to the standoff at the grocery store, the suspect allegedly shot his grandmother and girlfriend before fleeing in his car, CBS Los Angeles reported citing a police source.
U.S. President Donald Trump said he was watching the possible hostage situation very closely. "Active barricaded suspect. L.A.P.D. working with Federal Law Enforcement," Trump wrote on Twitter.