Rice was scheduled to leave Sunday night for a meeting in London and then travel to Brussels for a NATO gathering. On Wednesday, following the NATO meeting, she will travel to New Delhi, according to her new itinerary.
"Secretary Rice's visit to India is a further demonstration of the United States' commitment to stand in solidarity with the people of India as we all work together to hold these extremists accountable," White House press secretary Dana Perino said in a statement.
Rice had planned to attend the meeting of NATO foreign ministers Tuesday and Wednesday, with talks focusing on a broad international agenda, including Afghanistan, Georgia and the Ukraine. From there she was to visit Rome, Helsinki and Copenhagen, but it was unclear whether the trip to India would cancel or only postpone those visits.
Rice spoke with President-elect Barack Obama about India earlier on Sunday, McCormack said. It was the third phone conversation between the two since the attacks. Rice has also been in daily phone contact with Indian and Pakistani officials.
The announcement of Rice's trip came hours after Bush assured India's leader that the U.S. government will put its full weight behind the investigation into the attacks in Mumbai.
Earlier Sunday, a Republican senator endorsed a campaign suggestion from President-elect Barack Obama - appointment of a special envoy, perhaps former President Bill Clinton, to the disputed region of Kashmir - as the U.S. seeks to ease tensions between India and its nuclear-armed neighbor Pakistan.
The lone gunman captured by police after the attacks told authorities he belonged to a Pakistani militant group with links to Kashmir, a senior Indian police officer said. India has blamed "elements" from Pakistan for the 60-hour siege during which suspected Muslim militants hit 10 sites across India's financial capital, leaving at least 174 dead.
Bush told India's prime minister, Manmohan Singh, in a telephone call that "out of this tragedy can come an opportunity to hold these extremists accountable and demonstrate the world's shared commitment to combat terrorism," White House spokesman Gordon Johndroe said in a statement.
In addition to the Americans killed in the coordinated shooting rampage in India's financial capital, the foreigners among the dead included Germans, Canadians, Israelis and nationals from Britain, Italy, Japan, China, Thailand, Australia and Singapore.
Bush told the prime minister that "he has directed the state and defense departments along with other federal agencies to devote the necessary resources and personnel to this situation," Johndroe said.
Despite India's claim, Pakistan's ambassador to the United States, Husain Haqqani, said: "I don't think that this is the time for India or anybody in India to accuse Pakistan. It's time to work with Pakistan. Pakistan is now a democracy. India is a democracy.
And as two democracies, we need to strengthen each other, rather than fall into the trap of the terrorists, who want us to fight with each other so that they can get greater strength."
India repeatedly has accused Pakistan of complicity in terrorist attacks on its soil, many of which it traces to militant groups fighting Indian rule in the divided Himalayan territory of Kashmir.
The U.S. has tried to persuade Pakistan to shift its security focus from India, with which it has fought three wars, to Islamic militants along the Afghan border.
Obama told Time magazine in an interview in October that "Kashmir in particular is an interesting situation ... that is obviously a potential tar pit diplomatically." He spoke of devoting "serious diplomatic resources to get a special envoy in there to figure out a plausible approach." When asked if that sounded like a job for Clinton, Obama replied, "Might not be bad" and that they had spoken about the issue when they had lunch in September in Clinton's New York office.
The suggestion of sending an envoy won support from a leading Republican senator.
"I would think that might be a good idea because, it appears to me, that we have an interlocking situation of Afghanistan, Pakistan and India," said Sen. Richard Lugar of Indiana, top Republican on the Senate Foreign Relations Committee.
Asked specifically about Clinton as a possible mediator, Lugar said: "I think he could do a great job there."
Lugar and Haqqani appeared on ABC's "This Week."
