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Security officials say they have been warned by Indian and U.S. officials that a second attack on the Indian capital city New Delhi is possible.
Rice was to meet with Indian Prime Minister Manmohan Singh and other top officials.
Indian officials, facing public fury for failing to intercept the attack or end it quickly, have called on Pakistan to hand over a list of 20 suspected terrorists.
Pakistani President Asif Zardari said any of the 20 suspects wanted by India would be tried in Pakistan if there is evidence of wrongdoing.
Pakistan and India, which both have nuclear arsenals, have a history of enmity and have fought two wars.
Rice urged Pakistan to cooperate fully with India's investigation.
"I have said that Pakistan needs to act with resolve and urgency, and cooperate fully and transparently," Rice said during a press conference. "I know too this is a time when cooperation of all parties who have any information is really required." Indian anger -- at Pakistan, their own leaders, even the U.S. -- was clearly visible across the country today. There were street protests in Bangalore, Hyderabad and other cities, but the biggest was in Mumbai. Several thousand protestors holding banners and waving Indian flags gathered near the Gateway of India and the ravaged Taj Mahal Palace Hotel to protest the attacks on their city.
"This is the only way we can express our feelings," said Sinjay Ghad, 45. "The politicians are sleeping."
The businessman, wearing a "We Are United" flyer attached to his shirt, shouted "Our politicians are useless" along with several hundred others in one corner of the protest.
The nearby Taj Mahal Palace Hotel, where at least one terrorist held off Indian commandos through much of last weekend, is boarded up and smoke stains cover part of one side.
"We want peace in the city - not pieces of the city!" and "We would prefer a dog visit our house than a politician" were among the dozens of banners held by the protestors and peace marchers.
English teacher Suman Keluskar, 48, said the U.S. has inadvertently aided attacks on India by Pakistani militants.
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