The shootings happened at multiple locations in rural Northern California and it wasn't yet clear if the shooter was among the number of dead, the AP story said. The shooter himself has been killed by police and several victims are now being treated at a local hospital.
School officials took the uninjured children to a safe location as more than 100 law enforcement officials responded.
Two children were among the wounded, it was confirmed.
He said the gunman was a neighbor and had "been shooting a lot of bullets lately, hundreds of rounds, large magazines".
Several people were wounded at the school, said Jeanine Quist, an administrative assistant with the Corning Union Elementary School District.
There were a total of 10 people injured, and Tehama County Superintendent of Schools Rich DuVarney said no students or staff at the school were among the fatalities. The gunman was shot by officials, according to the sheriff's department.
Fox 5 in San Diego reports the shooting started at a home and moved to the elementary school.
The gunfire began around 8 a.m.in the community of Rancho Tehama Reserve, about 130 miles north of Sacramento.
A semi-automatic rifle and two handguns believed to be used by the gunman, who engaged police in a shootout, have been recovered, according to Johnston. California Gov. Jerry Brown issued a statement in the wake of the shooting: "Anne and I are saddened to hear about today's violence in Tehama County, which shockingly involved schoolchildren".