The Milwaukee Journal Sentinel said four of the dead were inside the temple in Oak Creek, Wis., and three of the dead were outside, including the gunman.
The newspaper, citing what it said was a source familiar with the investigation, reported the shooter was a white man in his 40s who had been discharged from the U.S. Army. The source said one firearm was recovered along with multiple magazines.
The Journal Sentinel reported FBI officials said Sunday night no motive had been determined for the shooting, though domestic terrorism was a possibility. Earlier, the newspaper said Oak Creek Police Chief John Edwards had labeled the shooting domestic terrorism.
Edwards said the gunman shot one Oak Creek officer who responded to the emergency call and was helping a victim. A second Oak Creek officer officer then fatally wounded the shooter, Edwards said.
Edwards said the wounded officer, identified as being at least a 20-year veteran of the department, was expected to survive.
The chief said at a 4 p.m. briefing that the temple had been secured.
Authorities also entered a home in Cudahy about 5 p.m. in connection with the shooting, the newspaper said.
WISN-TV said family members of temple President Satwant Kaleka said authorities had told them he was among the dead. Earlier reports had Kaleka being treated at an area hospital.
The Milwaukee TV station said officials at Froedtert Hospital said three men wounded in the shooting were still in critical condition as of 10:30 p.m. CDT Sunday.
While authorities had not identified any of the victims, temple attendee Manminder Sethi, a local dentist, told the Sentinel Journal one of those killed was a Sikh priest, Parkash Singh, who was in his mid 30s and had lived in Oak Creek for several years. Singh had recently returned to India to bring his wife, daughter and son to live with him in Wisconsin.
"He was a good guy, a noble soul," Sethi said.
One of the temple's committee members, Ven Boba Ri, said the gunman walked up to a priest outside the temple, shot him, then he went inside and resumed shooting, the newspaper said.
People inside the temple used cellphones to call for help, Ri said.
The White House released a statement by President Obama on the shooting.
"Michelle and I were deeply saddened to learn of the shooting that tragically took so many lives in Wisconsin. At this difficult time, the people of Oak Creek must know that the American people have them in our thoughts and prayers, and our hearts go out to the families and friends of those who were killed and wounded," the statement said.
The president said the administration "will provide whatever support is necessary to the officials who are responding to this tragic shooting and moving forward with an investigation. As we mourn this loss which took place at a house of worship, we are reminded how much our country has been enriched by Sikhs, who are a part of our broader American family."
WISN-TV reported Nirupama Menon Rao, India's ambassador to the United States, said in a post on Twitter, "Our hearts bleed for precious & innocent lives lost in Oak Creek. This is a very tragic time for our community. We must maintain calm."
Gov. Scott Walker issued a statement expressing sorrow for the victims and their families and thanks to authorities who responded to the shootings.
"Our hearts go out to the victims and their families, as we all struggle to comprehend the evil that begets this terrible violence," he said.
"At the same time, we are filled with gratitude for our first responders, who show bravery and selflessness as they put aside their own safety to protect our neighbors and friends."
Mitt Romney's campaign in Boston issued a statement in which the Republican presidential candidate and his wife Ann offered their thoughts and prayers to the victims.
"This was a senseless act of violence and a tragedy that should never befall any house of worship," Romney said. "Our hearts are with the victims, their families, and the entire Oak Creek Sikh community. We join Americans everywhere in mourning those who lost their lives and in prayer for healing in the difficult days ahead."
Lee Biblo, chief medical officer of Froedtert, said three men with gunshot wounds, including an Oak Creek police officer, were in critical condition at the hospital.
Darshan Dhaliwal, who described himself as a temple leader, said between 20 and 25 women were cooking a lunch in the basement and five to 10 children also were in the building when the shooting started.
Gurcharan Grewal, president of the Sikh Religious Society of Wisconsin told the Journal Sentinel reporter: "People are really shocked. There was a little bit of panic. But everything is holding together."
Grewal said the shooter's motivation was a mystery.
"Nobody knows," he said. "There was no indication, no warning, nothing. I think it was just some isolated hate crime or something. "
The newspaper said there are about 3,000 families in southern Wisconsin that practice the Sikh religion, which was started in India more than 500 years ago and has more than 20 million adherents worldwide.