Wade Michael Page, 40, was shot dead by police during the attack in a Milwaukee suburb, police said.
US officials said Wade Michael Page had been discharged from the military after being demoted.
Police will hold a press conference at 11:00 EDT.
A civil rights group, the Southern Poverty Law Center, has described Wade Michael Page as a “frustrated neo-Nazi”.
The organization added that in 2010 Wade Michael Page said in an interview with a white supremacist website that he had been a member of the white-power music scene in 2000, and created a band called End Apathy, the Associated Press reports.
The gunman, described by witnesses as a bald, white man, entered the Wisconsin Sikh Temple in Oak Creek on Sunday morning and opened fire.
He killed six people and critically injured three people, including a policeman, before another officer shot the attacker dead.
The wounded police officer was shot eight or nine times in the face and extremities at close range with a handgun. But he was expected to make a full recovery, police said.
Authorities said the gunman had used a 9mm semi-automatic pistol, which was recovered at the scene.
Wade Michael Page reportedly served in the US Army between April 1992 and October 1998, ending his career at Fort Bragg, North Carolina.
A federal official told the Associated Press news agency that Wade Michael Page was discharged after being reduced in rank from sergeant to specialist, although the official did not give a reason for the demotion.
According to US media, Wade Michael Page was a psychological operations specialist and a Hawk Missile System repairman.
He was reportedly disciplined in June 1998 for being drunk on duty, and discharged for “patterns of misconduct”.
Police said on Sunday they were treating the attack as an act of domestic terrorism.
But FBI Special Agent in Charge of the Milwaukee division, Teresa Carlson, said on Sunday night: “While the FBI is investigating whether this matter might be an act of domestic terrorism, no motive has been determined at this time.”
On Sunday night a warrant was issued allowing the authorities to search Wade Michael Page’s house in the town of Cudahy, a few miles from the temple.
Special Agent Thomas Ahern, of the Bureau of Alcohol, Tobacco, Firearms, told ABC News that Wade Michael Page had tattoos which might suggest the attack was a hate crime.
But a member of the temple told CNN the attacker had a 9/11 tattoo on one arm.
The names of the victims have not yet been made public, although the president of the congregation and a priest were reportedly among the victims.
The temple in Oak Creek was founded in 1997 and is said to have a congregation of about 400 worshippers.
Wisconsin, which passed a law in 2011 allowing citizens to carry a concealed weapon, has some of the most permissive gun laws in the US.
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