Heather Brent, a spokesperson for the San Joaquin County sheriff's office, said the children killed in Saturday's shooting were ages eight, nine and 14, while many others were wounded.
A 21-year-old also was killed in the attack in the city of Stockton.
"This was a birthday party for a young child, and the fact that this happened is absolutely heartbreaking," Brent said at a news briefing on Sunday.
The sheriff's spokesperson said the search continues for possible suspects. No arrests have been made.
Faith leaders in the Stockton area were planning a Sunday afternoon vigil to honour the dead and pray for the 11 people who were wounded.
Officials pleaded with the public for help. Detectives also were still working to identify a possible motive.
"If you have any information as to this individual, reach out immediately. If you are this individual, turn yourself in immediately," San Joaquin County District Attorney Ron Freitas said.
The shooting occurred just before 6pm inside the hall, which shares a parking lot with other businesses. Stockton is a city of 320,000 about 70km south of Sacramento.
Jason Lee, vice mayor and city council member, also said the hall was hosting a child's birthday party, according to his Facebook post.
"This is Thanksgiving weekend. This is when families come together, celebrate, share memories, give each other love," Mayor Christina Fugazi said.
"Unfortunately tonight, heaven is a little bigger with the individuals, children and adults that unfortunately did not make it."
Fugazi recalled a shooting several years ago in which "seven people were gunned down" in the city, adding that both attacks were "unacceptable".
"Stockton is better than this," she said.
Authorities did not immediately provide additional information about the conditions of the victims.
"Families should be together instead of at the hospital, standing next to their loved one, praying that they survive," Fugazi said.
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