At least four people, including three children, have been killed in a mass shooting at a family gathering in California, authorities say.

The victims were eight, nine, 14 and 21 years old, a spokesperson for the San Joaquin County Sheriff's Office said on Sunday. Eleven others were injured in the incident at a restaurant in the state's northern city of Stockton.

A suspect is still on the loose and police say they believe the shooting may have been "targeted".

The city's deputy mayor earlier said the shooting had occurred "at a children's birthday party". Police have not confirmed the type of event at which the shooting occurred, beyond it being a family gathering.

"[A] birthday party should never be a place where families fear for their lives," Deputy Mayor Jason Lee wrote on social media.

The San Joaquin County Sheriff's Office said the shooting happened shortly before 18:00 local time (02:00 GMT on Sunday), and is appealing to anyone with "information, video footage, or who may have witnessed any part of the incident" to come forward.

Spokeswoman Heather Brent described the incident as "unfathomable", adding: "This is a very active and ongoing investigation, and information remains limited.

"Early indications suggest this may be a targeted incident, and investigators are exploring all possibilities."

Stockton's Mayor Christina Fugazi called the shooting "unacceptable".

"Families should be together instead of at the hospital, standing next to their loved one, praying that they survive."

California has some of the strictest firearm laws in the US, and has in recent years faced challenges to it.

In 2021, a federal judge overturned the state's ban on assault weapons, such as the AR-15 rifle.

The following year, the US Supreme Court expanded gun rights as it struck down a New York law restricting gun-carrying rights, jeopardising similar regulation in California. (BBC)