The white supremacist gunman who killed six people at a Sikh temple in Wisconsin died of a self-inflicted gunshot wound to the head, the Federal Bureau of Investigation said today.

The gunman, Wade Page, 40, killed himself after a police officer shot him in the stomach outside the temple in Oak Creek, Wisconsin, on Sunday, FBI Special Agent in Charge Teresa Carlson told a news conference.

"Subsequent to that wound, it appears that Page died from a self-inflicted gunshot wound to the head," she said.

Police had said previously that Mr Page had been shot to death by an officer responding to the attack at the Sikh Temple of Wisconsin in suburban Milwaukee.

Ms Carlson said she had seen a video of the police gunshot that wounded Mr Page. "It's an amazing shot, and thank goodness," she said.

She said investigators had not found any motive for the rampage. Four people also were wounded, including a police officer shot eight or nine times at close range after responding to a 911 call.

Mr Page, an Army veteran, was a musician who played in white power punk-metal bands.

The dead were five men and one woman, aged between 39 and 84, including the president of the temple and a priest.