The gunman who killed six people at a Sikh temple south of Milwaukee on Sunday and critically wounded three others, including a police officer, was identified Monday as Wade Michael Page, a 40-year-old Army veteran with reported links to the white supremacist movement.

Page was shot and killed by a police officer outside the temple after he opened fire at Sikh worshipers and at police responding to the scene, Oak Creek Police Chief John Edwards said at a news conference.

Edwards said Page, who lived in a neighboring community, served in the military from 1992 to 1998, received a “general discharge” and was “ineligible for reenlistment.” A Pentagon official said Page rose to the rank of sergeant before being demoted to specialist and leaving the Army. News agencies reported that Page, who was never posted overseas during his six years of service, was discharged for being drunk on duty and other unspecified misconduct.

According to the Southern Poverty Law Center, a civil rights organization that monitors hate groups, Page was a “frustrated neo-Nazi who had been the leader of a racist white-power band.” He had been “part of the white power music scene since 2000,” when he left his native Colorado on a motorcycle, attended white power concerts in several states and played in a variety of “hate rock bands,” the center said, citing a 2010 interview Page gave to a white supremacist Web site about his latest skinhead band, “End Apathy.”

Edwards said Page shot the first police officer to arrive on the scene eight or nine times at close range with a handgun after the officer went to render aid to a victim of the shooting he found in the temple’s parking lot. The shooter also fired at two police cars and disobeyed commands to drop his weapon before an officer fatally shot him with a squad rifle, the police chief said.

He identified the wounded officer as Lt. Brian Murphy, 51, a 21-year veteran of the department. Murphy is in critical condition, Edwards said.

At the White House, President Obama was asked after a bill-signing ceremony whether he would pursue gun-control measures in the wake of the temple attack.

“We’re still awaiting the outcome of a full investigation,” he told reporters, adding that “all of us are heartbroken by what happened.”

Obama said such events happen with “too much regularity.” He said he would “examine additional ways to reduce violence” but stopped short of calling for new gun-control laws.

Referring to reports that the gunman may have been motivated by racial hatred, Obama said: “Regardless of what we look like, where we come from, or where we worship, we’re all one people.”

Because Sikh men typically wear turbans, they are sometimes mistaken for Muslims or Arabs, although they are neither.

Police said five Sikh men and one woman ranging in age from 39 to 84 were killed in the shooting rampage. Three other Sikhs were injured, and two are in critical condition, Edwards said. One was treated for an unspecified injury and released, he said.

Page “was the only shooter that was involved at the temple,” Edwards told reporters.

However, authorities also released a photo of an unnamed man, saying he was a “person of interest” whom they wanted to identify and question in connection with the shooting.

Earlier, Edwards said police were investigating reports that the shooter, who was white, may have harbored extreme racial views.

The Southern Poverty Law Center published on its Web site a photo of a man it said was Page, with a symbol commonly used by white supremacists and neo-Nazis tattooed on his left shoulder.

A Defense Department official said Page trained at Fort Sill, Okla., and served at Fort Bliss in Texas and Fort Bragg in North Carolina. Page worked as a repair technician for the Hawk missile system and later was detailed to Psychological Operations as a specialist, the official said.

Sunday’s mass shooting shocked the close-knit Sikh community and horrified Americans of all backgrounds, coming just two weeks after a deadly movie-theater rampage in Aurora, Colo., in which a gunman killed 12 people and injured 58. James Holmes, 24, has been charged in that massacre.

Volunteers had gathered early at the the Sikh Temple of Wisconsin, as they do every Sunday, to prepare Indian comfort food to nourish the faithful: lentils, yogurt, and rice pudding. It’s a ritual of inclusion that, according to those who return over and over, helps make Sunday prayers feel like a large family reunion.

“You feel like this is the safest place around,” said Kirandip Jawanda, 21, a data specialist at a local hospital.

But on this Sunday, terrified cooks and other early arrivers were forced into hiding after shots and screams broke their morning peace. Police said the gunman entered the temple and sprayed automatic-weapon fire, killing four people inside the building and two more outside.

In the news conference Monday, Edwards, the police chief, said the first 911 call about the shooting was received from inside the temple at 10:25 a.m. Sunday and that officers responded “within minutes.” He said Murphy, the first officer on the scene, “came upon a victim in the parking lot” and went to help the person. “He was met by the suspect, who basically ambushed him around his vehicle” and opened fire with a handgun while the officer was tending to the victim, Edwards said.

He said other officers arriving on the scene were initially unaware that one of their own had been shot. After fatally shooting Page, police found Murphy, who “waved them off” as they approached him and told them to go into the temple to assist the victims there, Edwards said.

He said it then took a long time to clear the scene because police initially did not know whether any other shooters were inside. They concluded that Page acted alone, Edwards said.

Police said a 41-year-old woman, Paramjit Kaur, was among those killed in the temple shooting. The other fatalities, all men, were identified as Sita Singh, 41; Ranjit Singh, 49; Satwant Singh Kaleka, 62; Prakash Singh, 39; and Suveg Singh Khattra, 84. Singh is a common surname for men in the Sikh religion.

The son of Suveg Singh Khattra, Balginder Khattra, said his father had been a farmer in northern India and had moved to Wisconsin in 2004, news agencies reported. He said his father did not speak English but loved living in America.

Local police said Page had no criminal record, and the FBI said it was not aware of any past threats against the temple.

Bernard Zapor, special agent in charge for the Bureau of Alcohol, Tobacco, Firearms and Explosives, said the weapon used in the shooting was a 9mm handgun that was purchased legally.

Federal and state agents are examining Page’s background, including whether he had posted anything on the Internet, law enforcement officials said, speaking on condition of anonymity because the investigation is unfolding. A semiautomatic pistol was recovered at the scene, officials said. Federal officials searched a home in nearby Cudahy, Wis. where the shooter may have lived.

The FBI is leading the investigation, with help from the Bureau of Alcohol, Tobacco, Firearms and Explosives and local police. Edwards said the shootings are being “treated as a domestic terrorist-type incident.” But federal law enforcement officials said it was too early to tell what happened and why.

“Right now, it’s just a mass shooting,” said a federal official who spoke on the condition of anonymity because he was not an authorized spokesman. “What you have is somebody who went into a Sikh temple and opened fire. Who knows what his motivation was?’’

The shooting started about an hour before attendance at the 15-year-old temple typically reaches its peak. Survivors were ushered across the street to the Classic Lanes bowling alley for law enforcement interviews. Frightened witnesses, mourners and others were joined by scores of supporters.

“I think some people misunderstand because we keep a long beard, and keep a turban. Some people think we’re al-Qaeda,” said Prem Paul, a Sikh truck driver from South Milwaukee who comes to the temple each weekend but arrived after the shooting.

Navdeep Singh, an official with the Sikh American Legal and Education Fund in Washington, said the community was “grateful for the brave and quick action of police officers, which prevented the tragedy from being even greater.”

“We are grateful for the outpouring of support that has come to our community, and we appreciate that we are seen as part of the American fabric.”

More than 500,000 adherents of the Sikh faith live in the United States, most of them first- or second-generation immigrants from India, where Sikhism was founded several centuries ago. Sikh men tend to stand out because of their beards and colorful turbans, which are ritually wrapped around uncut hair, and leaders in the community say they are sometimes confused with Muslims and viewed with suspicion.

After the attacks of Sept. 11, 2001, there were scattered reports nationwide of harassment or attacks on Indian Sikhs. In a misguided act of vengeance, a Sikh gas station owner in Arizona, Balbir Singh Sodhi, was killed.

Late Sunday, Tirlok Singh walked alongside Gurmel Singh, the grief-stricken head priest, whose brother-in-law was among the dead. Tirlok Singh gave raw voice to what many Sikhs said has been their predicament. “Tell the people we are not Muslim. We are different. We are Sikh. I want you to convey this message,” said Singh, who is also one of the temple’s priests.

Shiveharn Ghuman, 59, was among the Sikhs who rushed to Oak Creek from the Chicago area, about two hours to the south. The retired electrical engineer has a turban and beard, and in the aftermath of 9/11 experienced the taunts. “They said, ‘Hey, Osama. Go home,” he recalled.

Years earlier, when Islamic revolutionaries took Americans hostage in Tehran in 1979, such ugly sentiments also surfaced, Ghuman said. “It was scary at that time too. We had 13 windows broken in our temple” in Palatine, Ill., Ghuman said. Each one cost $2,500 to fix, a significant burden for a group planting its roots in America.

Sikhs are now more established, but still misunderstood. “Not too many people know who we are and what we believe,” Ghuman said. “We believe in one God, and earning your living, and sharing with the needy. These are the principles of our religion.”

In Oak Creek, until now, the Sikh temple had found a welcoming home amid the subdivisions, fields and strip malls. The temple was established in 1997 with 20 to 25 families. There are now 350 to 400 people in the congregation, according to the temple’s Web site.

Rakesh Kumar, a Hindu who prays at the Sikh temple, said Oak Creek residents of all sorts have joined in Sikh community picnics in the past. “It’s my neighborhood as well as my community. People are so loving. I love Oak Creek,” Kumar said. Now, however, people’s thoughts are turning to how “we should do more direction interaction” with the broader community.

Kirandip Jawanda said the temple is “where you come to try to release your stress. You work all week and come here on Sunday.” But now, her 10-year-old brother is too frightened to want to spend time there.

“It’s a fun place,” she said, “but I don’t know what it will be if people are all scared. I don’t know if people will come.”

President Obama and his Republican rival in the fall election, Mitt Romney, issued statements Sunday expressing condolences to the victims in Oak Creek and the Sikh community. Obama met with top federal officials and pledged federal assistance to Wisconsin.

Gurmel Singh, the head priest, said his brother-in-law Parkash Singh had only recently brought his family to the United States from India.

“He’s dead. Two children and a wife here,” Singh said. “I’m here for 15 or 16 years in the USA. And at this temple, maybe five years. There are no problems. First time problem.”

Charan Bedi rushed to the temple from Chicago, about 80 miles south, when he heard about the shootings. Family members who attend the temple were safe, but family friends were harmed.

“It’s a small community, so we know all of them,” Bedi said. “A loss between any family is a loss for all of us. The main question is, why?”

About 50,000 Sikhs live in the Baltimore-Washington region. Bhai Gurdarshan Singh, the high priest of a Sikh temple in Gaithersburg, was about to begin services Sunday morning when he was pulled aside and told of the shootings. He immediately informed his congregants and led them in a prayer for the victims.

“We are literally hurt, and we pray for the families,” he said.

Some congregants were particularly alarmed that the shootings took place while Sunday-school classes were going on. “It makes you question your own safety as an American in your own country,” said Daman Kaur, 26, of Frederick.

Markon and Branigin reported from Washington. Pamela Constable, Annys Shin and Julie Tate in Washington contributed to this report.