Law enforcement sources familiar with the investigation named him Monday as Wade Michael Page, 40. One law enforcement official said he owned the gun used in the shooting legally.
He had apparently served on active duty, a U.S. official familiar with his record said. The source declined to give further details.
The officials asked not to be named because they are not authorized to speak on the record about the shooting investigation. A police officer responding to the attack shot and killed the gunman, police said.
Relatives of Satwant Kaleka, the president of the temple in Oak Creek, Wisconsin, said Monday that he was killed fighting the attacker.
"From what we understand, he basically fought to the very end and suffered gunshot wounds while trying to take down the gunman," said Kanwardeep Singh Kaleka, his nephew.
"He was a protector of his own people, just an incredible individual who showed his love and passion for our people, our faith, to the end," he said, near tears.
"He was definitely one of the most dedicated individuals I have ever seen, one of the happiest people in the world."
Kaleka was horrified to have such violence occur at his place of worship, especially just two weeks after the 12 killings at a screening of the Batman movie"The Dark Knight Rises"in Aurora, Colorado.
"You're talking about Aurora one minute, and the next minute it's you and your family," Kaleka said.
"I just never thought it would be at a temple, at a place of worship. I don't want people to have to carry a gun at a place of worship," said Kaleka, who added that he could have been at the temple during the attack, but for the fact he had stopped at a bank "randomly to make a deposit."
"Why can't people just show each other love and care and treat each other as humans?" he asked.
Earlier, the FBI said that it had not determined a motive for the Sunday morning shooting and that investigators were looking into whether the attack might be classified as domestic terrorism.
Kaleka said those inside the gurdwara, or Sikh house of worship, described the attacker as a bald white man, dressed in a white T-shirt and black pants and with a9/11tattoo on one arm -- which "implies to me that there's some level of hate crime there."
Tom Ahern, a spokesman for theBureau of Alcohol, Tobacco, Firearms and Explosives, said the gunman had a military background but would not elaborate. He also would not elaborate on the man's tattoos.
Because of their customary beards and turbans, Sikh men are often confused with Muslims, and they have been the targets of hate crimes since theSeptember 11, 2001, attacks on New York and Washington.
While officials try to piece together what prompted the man to go on his shooting spree shortly before the main Sunday morning service, America's Sikh community struggled to come to grips Monday with the brutal attack.
"It's probably somebody not in their right mind," Justice Singh Khalsa, a temple member since the 1990s, said late Sunday. "It's possibly a hate crime, somebody not understanding the religion."
The victims ranged in age from their late 20s to about 70, said Khalsa, who helped translate witness accounts for authorities.
Three people remained in critical condition at Froedtert Hospital, the medical center said Monday.
