Peter Rodger, who was assistant director on The Hunger Games, thinks the attacker was his 22-year-old son Elliot, the statement said.
The gunman died of bullet wounds after going on a rampage near Santa Barbara.
Police are investigating a video in which Elliot Rodger complains of rejection by women, threatening revenge.
Authorities have not confirmed the identity of the gunman, or that of the young man seen in the YouTube video.
However, Peter Rodger’s lawyer, Alan Shifman, said on Saturday that the “family believes the child was the perpetrator”.
Alan Shifman said Elliot Rodger had Asperger’s syndrome, had trouble making friends and had been receiving professional help.
The lawyer added that the family had contacted police about “recent posts on YouTube” by Elliot Rodger “regarding suicide and the killing of people”.
The family is “devastated” and co-operating with police, he said.
Santa Barbara County Sheriff Bill Brown told reporters on Friday that police were treating the incident as “premeditated mass murder”.
It occurred in the area of Isla Vista, near the University of California-Santa Barbara campus.
Witnesses described seeing a black BMW speeding through the streets, with shots being fired at people.
Police say they were alerted around 21:30 on Friday. Six minutes later, the suspect and responding officers exchanged gunfire.
The suspect fled. But after a second exchange of fire with police, he eventually crashed into a parked vehicle.
The gunman was found dead in his car with a bullet wound to the head. Although police say it is not yet clear whether the wound was self-inflicted.
A semi-automatic handgun was recovered from the vehicle.
Seven other people are in hospital, and being treated for bullet wounds.
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