Wisconsin gunman Wade Michael Page
Wisconsin gunman Wade Michael Page, who opened fire on Sikh worshippers in their temple, killing six Reuters

Wade Michael Page, the gunman who shot dead six people in a Sikh temple in the US, died of self-inflicted wounds to the head, the FBI said.

Page, 40, killed himself after police shot him in the stomach outside the Oak Creek temple in Wisconsin, FBI special agent Teresa Carlson told a televised news conference.

Police had previously said he died after being shot by an officer.

Page, an army veteran who was said to belong to a white supremacist rock band, entered the Sikh temple and killed six people. He acted on his own, police said.

His former girlfriend, identified as Misty Cook, was arrested for illegal possession of a firearm, although there was no suggestion that she was involved in the temple attack.

Cook, a 31-year-old nursing student, ended her relationship in 2011, it emerged.

She declined to comment on the attack in an email to the Milwaukee Journal Sentinel newspaper.

"If I could say something to ease the pain of the victims and their families I would gladly do so.

"Unfortunately words do not begin to heal the pain they are going through," Cook wrote.