Earlier, speaking in London, Rice declined to comment on reports that a Pakistan-based group could be behind the co-ordinated attacks on two luxury hotels, a railway station and a Jewish centre.
"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.
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 [Indian] 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.
James Bays, Al Jazeera's correspondent in Mumbai, said: "The FBI are convinced that there were just 10 gunmen, who came to Mumbai by boat, and split up into groups of two.
"Some local press reports say they are now aware of the name of the mastermind of this operation. He was Yusuf Muzammil, a leader of Lashkar-e-Taiba. They say they have this information from the satellite phone left on board the boat."
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".
India has 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 attacks on parliament and commuter trains.
Pakistan has said it will "look at" the list of names and "frame a response".
|Some opposition groups in Pakistan have reacted angrily to India's accusations [EPA]
Mukherjee also said that it was not considering military action in response to the latest attacks in Mumbai.
"Nobody is talking of military action," Mukherjee said when asked about options on what action could be taken.
He 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 the Indian news channel NDTV.
"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 Lashkar-e-Taiba.
India's foreign ministry has said that New Delhi summoned Pakistan's high commissioner to inform him "that the recent terrorist attack on Mumbai was carried out by elements from Pakistan".
But Pakistan's government denies any links.
"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 news agency.
"Extremists have wanted India and Pakistan to be at each others' throats for a long time."