Police on Monday identified a 19-year-old California man as the gunman who opened fire with an assault rifle at a garlic festival in Gilroy, California, killing three people and wounding about a dozen.

Santino William Legan cut through a fence at the festival on Sunday evening and shot people, seemingly at random, with an "AK-47-style" assault rifle, Gilroy Police Chief Scot Smithee told reporters. Legan was fatally shot within about a minute by police.

"It could have gone so much worse so fast," Smithee said, noting that the festival, which takes place about 48 kilometers southeast of Silicon Valley, is ­attended by thousands of visitors.

Police and FBI agents were trying to determine a motive for the shooting and investigating unconfirmed reports by witnesses that Legan may have had an accomplice.

Smithee said that search warrants had been obtained for a home in Gilroy associated with the suspect and a car that police believe he drove to the festival.

Legan killed a 6-year-old boy, a 13-year-old girl and a man in his 20s, Smithee said. Police believe Legan, who was originally from Gilroy, purchased the rifle legally on July 9 in Nevada, where he had recently been living.

At least 11 people were treated for wounds, a spokesman for the Santa Clara Health System said in a recorded statement late on Monday.

Of those shot, five remained at the Santa Clara Valley Medical Center Monday night, he said. Of the five, three were in serious or fair condition and two wished to have no information released, he said.

Early police reports said that one person was in critical condition on Sunday.

Another 10 people received other, non-life threatening injuries, the hospital spokesman said, and were treated at St. Louise Regional Hospital.

Legan appeared to post a photograph from the festival on his Instagram account shortly before the shooting, with captions expressing his disdain for the event.

"Ayyy garlic festival time," he wrote beneath a picture of people walking through the festival grounds. "Come get wasted on overpriced shit."

Another photograph posted on Sunday showed a sign warning of a high danger of forest fires. Its caption urged people to read "Might is Right," a racist and sexist treatise written in the 19th century.

"Why overcrowd towns and pave more open space to make room for hordes of mestizos and Silicon Valley white twats?" the caption said, referring to people of mixed race. The account was only a few days old, and was deactivated on Monday.