In London on Tuesday, she declined to comment on reports that a Pakistan-based group could be behind the 60-hour bloodbath which left more than 171 people dead.
"I don't want to jump to any conclusions myself on this, but I do think that this is the time for a complete, absolute, total transparency and co-operation and that is what we expect," she said.
An Indian official said the death toll is expected to stand at 171 and that all bodies have been accounted for.
Bhushan Gagrani, the Maharashtra state government spokesman, said the dead include 26 foreign nationals.
He said the death toll would only increase if any of the 294 wounded succumbed to their injuries.
Pakistan ties
The White House said on Monday that it had no reason to doubt Pakistan's assertion that it was not involved in the shooting and bombings in Mumbai but Mike McConnell, the US director of national intelligence, said on Tuesday that the "same group that we believe is responsible for Mumbai had a similar attack in 2006 attack on a train and killed a similar number of people".
"Go back to 2001 and it was an attack on the parliament," he said in a speech at Harvard University.
McConnell did not mention Lashkar-e-Taiba by name, but the Pakistan-linked group, which opposes Indian rule in divided Kashmir, is widely blamed for a deadly assault on the Indian parliament in 2001 that pushed New Delhi and Islamabad to the brink of war.
Several Indian and US officials have met or are due to meet soon in a show of Washington's "solidarity" with New Delhi after what some have called "India's 9/11".
Shivshankar Menon, India's foreign secretary, met John Negroponte, the US deputy secretary of state, in Washington on Tuesday to discuss "our continuing co-operation to find and bring to justice the perpetrators of the Mumbai attacks", Gordon Duguid, a state department spokesman, said.
Besides Rice, Admiral Mike Mullen, the chairman of the US Joint Chiefs of Staff, is also travelling to the region to meet officials, Robert Gates, the US defence secretary, said on Tuesday.
On Monday, a US official said the Bush administration had warned the Indian authorities of the possibility of a waterborne attack on Mumbai.
The official would not elaborate on the timing or details of the US warning.
India demands suspects
Meanwhile on Tuesday, India demanded that Pakistan hand over 20 suspects it claims could be linked to the assault.
Pranab Mukherjee, India's foreign minister, said on Tuesday that New Delhi had asked for 'the arrest and handover of those persons who are settled in Pakistan and who are fugitive of Indian law".
India believes some of the 20 had links to other attacks in India, most notably the 2001 attack on its parliament and the 2006 multiple bombing of commuter trains in Mumbai.
Pakistan said it will "look at" the list of names and "frame a response".
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| Some opposition groups in Pakistan have reacted angrily to India's accusations [EPA] |
Mukherjee also said on Tuesday that it was not considering military action in response to the latest attacks in Mumbai.
"Nobody is talking of military action," Mukherjee told reporters when asked about options on what action could be taken.
Mukherjee said that peace talks with Pakistan, a process which started in 2004, would be difficult to continue after the attacks.
"We have no intention of not carrying out the peace process," he told Indian news channel NDTV.
But he added: "If these incidents ... are not adequately addressed by [Pakistan], it becomes difficult to carry out business as usual and that includes the peace process."
Indian investigators have said the attacks were carried out by the Lashkar-e-Taiba, a group based in Pakistan.
India's foreign ministry said New Delhi had summoned Pakistan's high commissioner to inform him "that the recent terrorist attack on Mumbai was carried out by elements from Pakistan".
The ministry said investigations had shown that all the attackers were Pakistani nationals.
Pakistan's response
Pakistan immediately hit back, with its foreign secretary summoning the Indian high commissioner in Islamabad to give a response to New Delhi's protest, the Press Trust of India reported.
Pakistan's government denies it was in any way linked to the attacks on India's financial capital.
"The target of this terrorist act was not just India. It was also Pakistan's fledgling democracy, and the India/Pakistan peace process," Husain Haqqani, Pakistan's ambassador to the US, told The Associated Press.
"Extremists have wanted India and Pakistan to be at each others' throats for a long time."