One of the dead was a priest named Prakash Singh, who recently immigrated to the United States with his wife and two young children, Khalsa said.
Authorities have not formally released the names of the deceased.
The three people who were wounded remained in critical condition early Monday morning at Milwaukee's Froedtert Hospital. One had been shot in the abdomen and chest, another in the face, and the third in the neck, the hospital 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 Monday. "India stands in solidarity with all the peace-loving Americans who have condemned this violence."
The country's main Sikh political party, the Shiromani Akali Dal, held a demonstration in New Delhi's embassy district Monday to protest.
"Stop racial attacks on Sikhs," read one of the placards.
In an act of solidarity, U.S. Ambassador Nancy Powell visited a historic Sikh shrine in New Delhi, embassy spokesman Unni Menon said.
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.
Women who were in the kitchen preparing meals for the congregants "were fortunate enough to basically duck down and dodge" the bullets, said Kanwardeep Singh Kaleka, the temple member.
Some ran to safety outside, others sought refuge in the temple's basement, while many huddled together tightly in the pantry.
The gunman shot and wounded the first officer to respond to the scene, Oak Creek Police Chief John Edwards said. A second officer returned fire, killing the shooter and bringing an end to the bloodshed, according to the chief.
A 9 mm semiautomatic pistol believed to have been used by the gunman was found at the scene, a law enforcement source with direct knowledge of the investigation said.
It took several more hours for authorities to thoroughly sweep the building and the surrounding area, checking for clues and signs of additional gunmen, as some witnesses had suspected.
Police spent Sunday night searching the shooter's home in nearby Cudahy, a short distance from the temple.
National and state political leaders, including Gov. Scott Walker, also offered condolences after the killings, which came two weeks after the massacre at a Colorado movie theater that left 12 dead and dozens more wounded.
Presumptive Republican presidential nominee Mitt Romney called the slayings "a senseless act of violence and a tragedy that should never befall any house of worship."
And from the White House, President Barack Obama said the United States had been "enriched" by Sikhs, "who are a part of our broader American family."
"My administration will provide whatever support is necessary to the officials who are responding to this tragic shooting and moving forward with an investigation," he said.
The Sikh religion originated in northern India around 1500 and has about 25 million followers.
The United States is home to about 700,000 Sikhs, nearly all of Indian origin. The men are easily identifiable by their beards and turbans, a tradition that's lasted for 500 years.
But the attire and appearance have also meant that they are often mistaken for Muslims and are targets of anti-Islamic attacks from those who seek to avenge the September 11 attacks.
The first person murdered in retaliation for the 9/11 attacks was a Sikh -- Balbir Singh Sodhi, a gas station owner in Mesa, Arizona. He was shot five times by aircraft mechanic Frank Roque on September 15, 2001.
In the intervening years, the Sikh Coalition, a New York-based advocacy group, reported more than 700 attacks or bias-related incidents.
Indiana Gov. Mitch Daniels issued the following statement regarding Sunday's shootings:
“Any attack of such brutality angers and saddens us, but the murders in Milwaukee yesterday were especially heartbreaking and ironic. I have long known many members of Indiana’s Sikh community; I have attended services at their temple. They are among the most productive and communitarian of all our citizens and theirs is a faith of gentleness and toleration. I know the hearts of Hoosiers are with those directly harmed and with their Sikh brethren here among us, for whose daily practice of loyal citizenship we are deeply grateful.”