The six victims of Sunday's attack were identified by police as five men -- Sita Singh, 41; Ranjit Singh, 49; Satwant Singh Kaleka, 65; Prakash Singh, 39, and Suveg Singh, 84 -- and one woman, 41-year-old Paramjit Kaur.
Two other Sikh victims remained hospitalized in critical condition, while a third was treated and released, Edwards said.
Prayer vigils were held Monday night in the Milwaukee metropolitan area, with another scheduled for Tuesday evening.
The wounded police officer, identified as 51-year-old Lt. Brian Murphy, also was in critical condition, the police chief said. Edwards told CNN's "Erin Burnett OutFront" that Murphy had a "promising," but long, recovery ahead. The officer suffered nine gunshot wounds.
One of the dead, Prakash Singh, was a priest who recently immigrated to the United States with his wife and two young children, said Justice Singh Khalsa, a temple member since the 1990s.
Relatives of Kaleka, the president of the temple in Oak Creek, Wisconsin, said 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.
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 the 9/11 tattoo on one arm, which "implies to me that there's some level of hate crime there."
While officials try to piece together what prompted the man to go on his shooting spree, America's Sikh community struggled to come to grips with the brutal attack.
A Sikh human rights group said it would give a $10,000 reward to Murphy, the police officer wounded in the attack.
"Our government must take urgent steps to educate the country about the Sikh population and help put an end to these horrific and deadly acts of violence," said a statement by the group, Sikhs for Justice.
Kaleka was horrified to have such violence occur at his place of worship, especially so soon 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.
Meanwhile in India, the birthplace of Sikhism, Prime Minister Manmohan Singh said he was "shocked and saddened" by the shooting.
"That this senseless act of violence should be targeted at a place of religious worship is particularly painful," Singh, himself a Sikh, said.
The country's main Sikh political party, the Shiromani Akali Dal, held a demonstration in New Delhi's embassy district Monday to protest.
Secretary of State Hillary Clinton spoke by phone with India's foreign minister, and U.S. Ambassador Nancy Powell met with Sikh community leaders in New Delhi and visited the largest Sikh temple in the city, said State Department spokesman Patrick Ventrell.
Sunday's 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. The temple has more than 350 members.
According to witnesses, the gunman started shooting in the parking lot, killing at least one person. He then entered the temple and continued firing, they said. Police spent Sunday night searching the shooter's home in nearby Cudahy, a short distance from the temple.
Political leaders at the national, state and local level offered condolences for the killings and declared solidarity with the Sikh community.
Obama ordered U.S flags flown at half-staff through Friday "as a mark of respect for the victims of the senseless acts of violence."
In a statement Sunday, Obama said the United States had been "enriched" by Sikhs, and that his administration "will provide whatever support is necessary to the officials who are responding to this tragic shooting and moving forward with an investigation."
Romney, meanwhile, called the slayings "a senseless act of violence and a tragedy that should never befall any house of worship."
The United States is home to about 700,000 Sikhs, nearly all of Indian origin, according to the Sikh American Legal Defense and Education Fund. The men are easily identifiable by their beards and turbans, a tradition that's lasted for 500 years.