Police officers investigate the scene of a shooting at the church in Sacramento, California, on Monday. AFP

A father shot and killed his three daughters, their chaperone and himself during a supervised visit with the girls on Monday at a church in Sacramento, police said.

Deputies responding to reports of gunfire around 5pm found five people dead, including the shooter, at the church in the Arden-Arcade neighbourhood, said Sgt. Rod Grassmann with the Sacramento County Sheriff’s Office.

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A fifth person also died in the shooting in Sacramento, California, though it was not clear if that person was related to what police said was a domestic incident.

Sacramento County Sheriff’s deputies gather at a church in Sacramento, California, on Monday. AP

All three children who died were under the age of 15, Sergeant Rod Grassmann of Sacramento County Sheriff's Office told reporters.

"At 5:07 this afternoon, we received a call that there was a shooting inside the church," Grassmann said.

"We have found now there's an adult male, a father who has shot and killed his three children under the age of 15," he added.

"And my understanding is that there is a fifth person that is also deceased. I don't know if they are related."

An investigator works following a shooting in Sacramento, California, US, on Monday. Reuters

An employee of The Church In Sacramento heard the gunshots and called 911, Grassmann said.

Sheriff’s officials are investigating it as a domestic violence incident, he said.

Officials didn’t know if the family members belonged to the church, which sits on a mostly residential block near a commercial area east of downtown Sacramento.

The shooter’s name wasn’t immediately released, but officials said he was 39 years old.