LOS ANGELES • A gunman took hostages inside a supermarket in Los Angeles after a gun battle with police, leaving a store employee dead before the suspect handcuffed himself and surrendered, police said.

The ordeal began at around 1.30pm last Saturday, when the suspect shot his grandmother as many as seven times, police chief Michel Moore told reporters. The suspect also shot and injured another woman, whom he kidnapped in his car, Mr Moore said.

The suspect fled from the police in a 2015 Toyota Camry and, at one point, began shooting at officers from his car, the authorities said.

He crashed his car outside the Trader Joe's supermarket, where he exchanged more gunfire with police and entered the crowded store.

Armed with a handgun, he took about 40 people hostage inside the store, including children, shoppers and employees, the authorities said.

"Inside the store, a young woman was shot and killed," Mr Moore said, adding that officers rescued her, but she could not be revived.

There were contradictory reports about whether the victim, whom US media identified as store employee Melyda Corado, was shot by the gunman or in the crossfire with the police.

During the standoff, aerial footage from TV stations NBC Los Angeles and CBS Los Angeles showed people leaving a store window using a rope ladder and police carrying children to safety through a parking lot in the city's Silver Lake neighbourhood.

After the standoff began, the area was locked down and streets were filled with police cars and firetrucks. During the earlier shootout, the suspect was wounded in the arm, Mayor Eric Garcetti said.

The authorities rescued some hostages, and the gunman released others, officials said. Finally, after about three hours, the suspect handcuffed himself and surrendered, the authorities said.

The grandmother had surgery and was in critical condition, Mr Garcetti said.

Mr Devin Field, who said he was walking into the store when the incident unfolded, described his experience in a series of tweets.

"I was walking in when a car... running from the police crashed into street lamp in front of the entrance.

"Gunman got out and started shooting at the cops. I hid behind a retaining wall with three cops until they had me crawl out," wrote Mr Field, whose Twitter account identifies him as a writer for the TV show Jimmy Kimmel Live.

"Gunman walked in shooting. He went into the back and took hostages. Employees snuck out through back emergency exits. Employee says blood was all over the floor, unclear from where," he wrote.

The situation drew the attention of President Donald Trump, who tweeted at one point during the standoff that he was watching it "very closely".

AGENCE FRANCE-PRESSE, REUTERS, NYTIMES