At least four people, including three children, have been killed in a mass shooting at a children’s birthday party 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. Eleven others were injured – one critically – in the incident at a restaurant in the state’s northern city of Stockton.

A suspect is still on the loose. Authorities say they believe the shooting may have been “targeted” and may have been committed by multiple people.

The city’s deputy mayor said the attack had occurred “at a children’s birthday party”. Police had previously described the event as a family gathering.

Heather Brent, a spokeswoman for the San Joaquin County Sheriff’s Office, confirmed to BBC News on Monday that the gathering was a children’s birthday party.

No additional details were provided, but a neighbour told the Los Angeles Times that the party was for a 2-year-old.

“[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.

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”. She added: “Families should be together instead of at the hospital, standing next to their loved one, praying that they survive.”

On Sunday, the mayor said she would match a $10,000 (£7,569) reward for any information leading to an arrest and conviction. Stockton City Councilwoman Mariela Ponce also offered $5,000, bringing the total bounty to $25,000.

People who live nearby told local news outlet KCRA 3 they heard gunshots for about a minute, and that they heard more than one person firing.

Sheriff Patrick Withrow, also from the San Joaquin County Sheriff’s Office, said “we believe… there appears to be multiple shooters” but that detectives needed to confirm as much.

One man, Emmanuel Lopez, told the LA Times that his brother Susano Archuleta was the 21-year-old man who had been killed, saying he had been hit in the neck and died at the scene.

“I’m just upset right now. My brother died in my arms,” Lopez told the newspaper. He said Mr Archuleta had been “full of life and energy”.

Mr Lopez also said his 9-year-old daughter had been among those who were injured but survived, having been shot in the head during the assault.

Patricia Flores identified herself as the aunt of Mr Archuleta. She was quoted by the BBC’s US partner CBS saying: “He was a good kid and he went to the celebration for a friend of his, it was his friend’s daughter, I believe.”