For her part, Rice called on Pakistan to give its "full co-operation" and show transparency in finding those responsible for the attacks on India's financial capital.
Relations between India and Pakistan have been brought into sharp focus since the attacks on two luxury hotels, a railway station and a Jewish religious centre, with New Delhi accusing Pakistani individuals of being involved.
At least 171 people were killed and more than 300 injured in the assault.
"I found the Pakistani leadership very focused and committed to act," she said after talks with Asif Ali Zardari, the Pakistani president, and Yousuf Raza Gilani, the prime minister, and senior army officials.
Zardari promised Rice that his government would take "strong action" against Pakistani elements found involved in the attacks.
"The government will not only assist in investigation but also take strong action against any Pakistani elements found involved in the attack," an official statement issued after their meeting said.
"It just has to be a robust response and one that is effective" in bringing the attackers to justice, Rice said.
"But I've also been emphasising the importance of prevention here.
"The Pakistanis are sophisticated; they've been dealing with terrorism themselves for some time. So I'm going there to talk about a Pakistani response, not to carry messages."
Rice met Pranab Mukherjee, the Indian foreign minister, after arriving in New Delhi on Wednesday, before going on to meet Manmohan Singh, the country's prime minister.
Against this backdrop of rising tensions, India has put all its major airport on high alert, in response to warnings of possible attacks using hijacked aircraft.
The government had ordered extra checks to vehicles and luggage after warnings from intelligence agencies, officials said on Thursday.
Local television showed armed police guarding entrances to Delhi's international airport. Police cordons had also been set up outside the airport in the southern industrial city of Chennai.
The developments come a day after thousands of people held a vigil in in Mumbai, close to the Taj Mahal Palace hotel, where one of the bloodiest attacks occurred.
Many of those at the vigil say that neighbouring Pakistan is responsible for the attacks.
As the remembrance event went ahead, the head of the country's counter-terrorism force said that Mumbai police had found and defused two bombs.
The explosives were found hidden in a bag at the Chhatrapati Shivaji railway station on Wednesday, a week after it came under deadly attack by armed men who also targeted several other buildings in the city.
While searching 150 bags at the station, police found one that looked suspicious and called the bomb squad. They found two bombs of 4kg each inside and defused them, police said.
"This is part of the same consignment which the terrorists had brought on Wednesday night [a week ago] when they were attacking and running helter-skelter, some of the material had been left behind," KP Raghuvashi, India's counter-terrorism chief, said.
Indian investigators have said the Mumbai attacks were carried out by Lashkar-e-Taiba, a Pakistan-linked group.
Mukherjee 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".
|Some opposition groups in Pakistan have reacted angrily to India's accusations [EPA]
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".
Mukherjee also said that New Delhi is 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.
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 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."
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.