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.