The gunman who killed six people at a Sikh temple in the U.S. died of a self-inflicted gunshot wound to the head after he was shot by police, the FBI announced.

Wade Michael Page, 40, is seen in this undated picture from a myspace.com web page for the musical group End Apathy. Police say he killed himself after his shooting rampage. (Myspace.com/Reuters )

FBI Special Agent in Charge Teresa Carlson told a news conference Wednesday that investigators have not yet "clearly defined a motive" for Sunday's shooting at the Sikh Temple of Wisconsin.

Authorities previously said an officer had fired the shot that killed gunman Wade Michael Page.Authorities haven't identified anyone other than Page as being responsible for the attack.

Temple members have said the temple had never received any threats, and Page had not been seen at the temple in the past.

U.S. President Barack Obama called Indian Prime Minister Manmohan Singh on Wednesday to express his condolences, White House press secretary Jay Carney said. Singh is India's first prime minister from the Sikh faith, and several victims were from India.

Carney said the two leaders discussed their "shared commitment to tolerance and religious freedom."

Carlson said federal officials had not opened any investigation into Page before the shooting. She said investigators were interviewing dozens of people who have known Page as they worked to determine a possible motive.

"We just want to get to the bottom of what motivated him to do it," said Amardeep Singh, an executive with the New York-based Sikh Coalition. "It's important to acknowledge why they lost their lives."

The 40-year-old army veteran strode into the temple shortly before Sunday services and opened fire with a 9-mm pistol. The dead included temple president Satwant Singh Kaleka, who was shot as he tried to fend off the shooter with a butter knife.Page wounded a responding police officer in the parking lot before another officer shot Page.

'Frustrated neo-Nazi'

The Southern Poverty Law Center has described Page as a "frustrated neo-Nazi" who participated in the white-power music scene, playing in bands called Definite Hate and End Apathy.

If investigators conclude Page was motivated by racist ideology, that might lead police to accomplices and prevent future attacks.

Rajwant Singh, chairman of the Sikh Council on Religion and Education, said even though Page is dead, other white-supremacy and neo-Nazi groups could harbour similar intentions.

"Our concern is, how do we tackle these hate groups operating underground or in darkness?" he said.

The FBI has classified the incident as domestic terrorism, a violent act for social or political gain.

Page had a record of minor alcohol-related crimes in Texas, Colorado and North Carolina. He was demoted during a stint in the army for getting drunk on duty and going absent without leave before he was discharged in 1998.

Page eventually moved to Wisconsin, living with a girlfriend and working at a factory.

Neighbours said the couple broke up this past spring. Page quit showing up for work in July. He visited a gun shop and, after clearing background checks, bought the gun he used in the shooting.

The investigation could take weeks or longer.

Page's girlfriend, 31-year-old nursing student Misty Cook, was arrested on a tentative charge of being a felon in possession of a firearm, South Milwaukee police said Tuesday. The FBI said Wednesday her arrest was not linked to Sunday's shooting.