The Indian media have said he is linked to the militant group Lashkar-e-Toiba, but the group has denied responsibility.
Although he did not mention Lashkar-e-Toiba by name, the US Director of National Intelligence said the militant group the US suspects carried out the Mumbai attacks was the same one that was behind the train blasts in the city in July 2006 that killed 186 people.
"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," Mr McConnell said in a speech at at Harvard University. "Go back to 2001 and it was an attack on the parliament."
Lashkar-e-Toiba was blamed by the Indian government for the 2006 train bombings, along with the Students' Islamic Movement of India (Simi), and for the parliament attack, in which 12 people died.
Correspondents say the alleged US intelligence warning is likely to add to growing public anger that they were not prevented.
India's home minister and the chief and deputy chief ministers of Maharashtra state have all resigned.
India's NDTV has broadcast CCTV from inside Chhatrapati Shivaji Terminus on the night of the attacks
Chief of the Naval Staff Admiral Suresh Mehta said on Tuesday that failures needed to be "taken stock of", but he added that the government's response was "going to be quite adequate".
Foreign Minister Pranab Mukherjee said a military response was not under consideration but that if Pakistan did not act the bilateral peace process would be at risk.
India has also asked Islamabad to hand over 20 fugitives from Indian law it believes are hiding in Pakistan. It is not clear what, if any, links those on the list had to the Mumbai attacks.
Indian media reports say the names include alleged underworld don Dawood Ibrahim, wanted in connection with bombings in Mumbai in 1993, and Muslim cleric Maulana Masood Azhar who was freed from jail in India in exchange for passengers on a hijacked plane in 1999.
Islamabad has not responded directly to the request but on Tuesday offered India a joint investigation into the attacks.
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