A gunman in the US state of California shot and injured two children aged six and five at a school before fatally shooting himself, in what police said was a targeted attack.

The children are in critical but stable condition and were being treated at a trauma centre, officials said in an update on Thursday.

The attack happened at a school affiliated with the Seventh-Day Adventist Church near Oroville, California, about 55 miles (89km) from Sacramento.

Investigators said they believe the gunman targeted the school because of its affiliation with the church and was motivated as a response to the war in Gaza.

The shooting occurred shortly after 13:00 local time (21:00 GMT) on Wednesday at the Feather River School of Seventh-Day Adventists.

Butte County Sheriff Kory Honea said the gunman, Glenn Litton, 56, had scheduled a meeting with a school administrator to discuss enrolling a student, which Honea called a "guise" to gain access to the school.

The meeting was seemingly cordial and Litton went on a tour, Sheriff Honea said, but things took a turn when the gunman walked towards a bathroom and started opening fire. The gunfire hit students outside a classroom, striking two kindergarten-aged children.

The gunman then turned the handgun on himself, police said. He was found dead by first responders with the firearm near his body.

The school's remaining 35 children were later transferred to a church, where they were reunited with their families.

Sheriff Honea said on Wednesday that the young victims had "very, very serious" injuries.

"I'm thankful that they are still alive but they have a long road ahead of them."

The sheriff on Thursday said a note was found detailing the gunman's motive. The note said he carried out the "child executions" as a "response to America's involvement with Genocide and Oppression of Palestinians along with the attacks towards Yemen".

Authorities said the gunman had a lengthy mental health and criminal history, which included charges of theft, fraud and forgery over the years.

Sheriff Honea previously said investigators "have received some information that leads us to believe that the subject responsible for the shooting targeted this school because of its affiliation with the Seventh-Day Adventist Church".

He previously noted authorities believed the shooting was an isolated incident, but a state-wide alert was sent to other schools affiliated with the Seventh-Day Adventist Church out of an abundance of caution.

The church is a Protestant Christian denomination with over 21 million members worldwide. There are one million members of the church in North America, according to the North American Division of Seventh-Day Adventists.