A teenage boy who killed two classmates and wounded three others at a southern California high school on his birthday before shooting himself in the head died on Friday of his wounds in hospital, the Los Angeles County Sheriff's office said.

"Nathaniel Tennosuke Berhow, 16, a Junior at Saugus High School, was being treated for a self-inflicted gunshot wound to the head, when he succumbed to his injuries. His mother was present at the time of his passing," the sheriff's office said in a written statement.

The boy was carrying out a deliberate plan when he shot five students at his California high school, then turned the gun on himself, a local sheriff said on Friday, but authorities said they had no clues about what sparked the bloodshed.

Two of the other five students who were shot in the Thursday morning attack at the school in Santa Clarita died of their wounds.

"We did not find any manifesto, any diary that spelled it out," Los Angeles County Sheriff Alex Villanueva said at a briefing.

The gunman was publicly identified by law enforcement for the first time on Friday as Nathaniel Tennosuke Berhow.Berhow initially survived his self-inflicted gunshot wound but died at a local hospital on 3:32pm. on Friday, according to the sheriff's department.

Detectives worked through the night to follow up on tips related to the shooting in Santa Clarita, about 65 kilometres north of Los Angeles. The incident, which was caught on video, unfolded in 16 seconds, police said.

Origin of gun

Arriving at school on his 16th birthday, Berhow pulled a .45 semi-automatic pistol from his backpack in an outdoor courtyard, stood in one place and shot his victims in rapid succession before turning the gun and firing the last bullet into his head.

Villanueva said authorities did not know the origin of the gun used, or how the gunman got his hands on it.

All Hart District schools in Santa Clarita were closed on Friday, the Santa Clarita Valley Sheriff's office said on Twitter, out of respect for the victims and their families.

Two girls aged 14 and 15 were being treated at Providence Holy Cross Medical Center in Mission Hills, California, and were listed in good and fair condition, a hospital spokeswoman said early on Friday.

At the Henry Mayo Hospital in Santa Clarita, authorities said a 14-year-old boy was treated and released. Two other students who had been taken there died. A hospital spokesman could not immediately be reached on Friday.

Villanueva identified one of the students killed as Gracie Anne Muehlberger, 15. He said the families of the other student killed and those wounded did not authorise him to release their names.

The scene at Saugus High School was reminiscent of other mass shootings at United States schools, including Marjory Stoneman Douglas High School in Parkland, Florida, where a former student with an assault rifle killed 17 people on February 14, 2018.

It was the 85th incident of gunfire at a school this year, according to Everytown, a gun control advocacy group.