The FBI has begun investigating the killing to determine whether it was an act of domestic terrorism but no motive has been determined.
FBI officials also confirmed Sunday night that they are investigating a home in Cudahy, Wisconsin - presumably that of the shooter - in relation to the incident, the Milwaukee Journal Sentinel reported.
It is not clear whether it was domestic terrorism, US Attorney James Santelle was quoted as saying. "My focus is not on what category it is but what happened and the loss of life in Oak Creek," he said.
Oak Creek police officers who responded to a 911 call about the shooting were helping a victim when the shooter ambushed one of the officers, shooting the officer multiple times. A second Oak Creek officer returned fire, killing the shooter, Edwards said.
Investigators, who picked through the building afterward, found four bodies inside the temple and two other victims outside, plus the gunman, Wentlandt was quoted as saying by CNN.
All three of the wounded were in critical condition at Milwaukee's Froedtert Hospital, spokesperson Carolyn Bellin told CNN. The congregation's president was among the wounded, his nephew Kanwardeep Singh Kaleka said.
Law enforcement personnel outside the Sikh Temple of Wisconsin . Photo: AFP
Though early reports had suggested there may have been more than one attacker, he said officers had not identified any other gunmen.
The wounded officer, a 20-year veteran, was in surgery Sunday afternoon after being shot multiple times, but was expected to survive, Wentlandt said.
Police did not release information about the gunman, with Edwards saying, "That is being checked into and is part of the criminal investigation." Nor would he disclose specifics of why the attack was being classified as an act of domestic terrorism.
The attack occurred about 10.30 a.m., when temple members were reading scriptures and cooking food in preparation for the main Sunday service and community lunch, Kaleka said.
Kaleka, who helped police interview witnesses, said members described the attacker as a bald, white man, dressed in a white T-shirt and black pants and with a 9/11 tattoo on one arm -- which "implies to me that there's some level of hate crime there".
A law enforcement official confirmed to CNN the shooter was wearing a white T-shirt and did not have a bulletproof vest.
CNN cited Teresa Carlson, special agent in charge at the FBI's Milwaukee division, as saying late Sunday that while authorities are looking into whether this "might be an act of domestic terrorism, no motive has been determined at this time."
White House officials said President Barack Obama was notified of the shootings shortly before 1 p.m. by John Brennan, his Homeland Security adviser. The president continues to receive updates.
After receiving a briefing at 4.30 p.m. from Brennan, FBI Director Bob Mueller, Chief of Staff Jack Lew, Obama called Governor Scott Walker, Oak Creek Mayor Steve Scaffidi and trustee of the Sikh Temple Charanjeet Singh to express his condolences for the lives lost and his concern for those who were injured.
Police searched the suspect's home, "a short distance" from the temple, Sunday evening, according to a law enforcement source cited by CNN. A single semi-automatic pistol believed to have been used by the gunman was found at the scene, along with the wounded officer's weapon, the source said.
Initial reports were that there may have been multiple attackers, but police found no indication of another gunman, said Bradley Wentlandt, the police chief in nearby Greenfield.
Congregation president Satwant Kaleka was shot and wounded when he attempted to tackle the gunman, his son, Amardeep Kaleka told local TV station WTMJ. His mother -- who hid in a closet during the violence -- was too distraught to talk, he said.
A hotline has been established for family members looking for information on those involved. The number is (888) 298-1964.