At least four people have been killed and 10 wounded following a shooting rampage at several locations, including an elementary school, in Northern California on Tuesday morning, according to media reports.

The shooting occurred around 8 a.m. in Rancho Tehama, about 200 kilometers northwest of Sacramento, the state capitol. The gunman was killed by police, authorities were quoted as saying.

The 10 wounded -- including two children -- are being treated at a hospital.

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The gunman randomly targeted people and property in seven locations, USA Today reported, citing an undersheriff of the local sheriff's office. The shooter was armed with a semi-automatic rifle and two handguns.

Police did not give immediate word on the assailant's motive for the shooting but a sheriff's official said the gunman's neighbors had reported a domestic violence incident, according to the Associated Press.