U.S. authorities say they are investigating possible ties between the gunman who killed six worshippers at a Sikh temple in Wisconsin and white supremacist groups.

Officials Monday identified the shooter, who was killed by police, as 40-year-old Wade Michael Page. They say he served in the U.S. Army for about six years in the 1990s before being discharged for misconduct.

A U.S. group that monitors extremists says Page was a member of a white supremacist band called End Apathy.

Authorities say they are looking into his links to supremacist groups, and say the shooting is being investigated as an act of domestic terrorism. They say they do not believe anyone else was involved in the attack, which took place Sunday morning near the city of Milwaukee.

Sikhs, who wear turbans and beards, have been mistaken in the United States for Muslims and sometimes targeted for hate crimes, including a Sikh who was killed in the state of Arizona four days after the September 11, 2001 terrorist attacks.

President Barack Obama said “soul searching” is needed about how to reduce violence in America. He said Americans would “recoil” in shock if it turned out the shooter was motivated by ethnic hatred.

The president ordered flags at federal buildings to be flown at half-staff through Friday.

Indian Prime Minister Manmohan Singh, himself a Sikh, said he was shocked and saddened by the assault, calling it a “dastardly attack.” India is home to a majority of the world's Sikhs.

“It is a very sad occasion, senseless killings of people who gathered together in a religious congregation. That it has happened in very tragic circumstances is something which makes me enormously sad. I hope the American authorities would investigate who were behind this dastardly attack on innocent devotees and that they will ensure that such costly events do not take place.”

Authorities say the gunman killed the six worshippers — five men and one woman ranging in age from 39 to 84 — before he was shot dead by police.

Investigators said three others were hospitalized in critical condition with severe gunshot wounds, including a policeman who was shot eight or nine times before a second policeman killed Page.

Sikhism is a monotheistic religion founded more than 500 years ago in the Punjab district of what is now India and Pakistan.

Authorities say the worldwide population of Sikhs is 20 million, with 400,000 to 1 million Sikhs in the U.S.