Officials are telling residents in the Rancho Tehama area to stay inside their homes until they are able to secure the situation.
Details were still sketchy hours after the shooting and authorities didn't have a firm count of the wounded due to the number of places where the gunman opened fire in the community of Rancho Tehama Reserve, about 130 miles north of Sacramento, Tehama County Assistant Sheriff Phil Johnston said.
The shooter was killed by police, bringing the total death toll to five.
The shooter reportedly wounded kids at the school.
Quist said about 10:30 a.m. local time that parents were able to get to the school to see their children.
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Another witness, Casey Burnett, said the gunman was "driving around and shooting randomly from his auto".
Remington manufactured the military-style assault rifle used in the 2012 massacre at Sandy Hook Elementary School that killed 20 children and six adults. Mercy Dignity Health confirmed that the hospital has received three patients.
He said that two officers shot at the suspect upon encountering him, and have since been removed from the scene. A woman and another child were shot in a truck that was driving near the school and taken to the hospital, he added.
Rancho Tehama Elementary is a small school, serving students in pre-kindergarten through fifth grade.
Gov. Jerry Brown issued a statement offering condolences to families who lost loved ones in "today's violence in Tehama County, which shockingly involved schoolchildren".