A group calling itself the "Deccan Mujahedeen" claimed responsibility for the attacks late Wednesday night on the Taj Mahal and Oberoi Trident hotels, and eight other locations, including the main train station, a hospital and an up-market restaurant.
Maharashtra state's Director General of Police A N Roy said around 100 people were killed in the precisely targetted assaults by small groups of gunmen armed with AK-47s and grenades that began around 10:30pm (1700 GMT).
Some foreign tourists were reported to be among the dead.
Witnesses said the gunmen had specifically chosen US and British citizens to take hostage.
Frequent bursts gunfire in and around the two five-star hotels continued to be heard on Thursday morning.
The head of Mumbai's Anti-Terrorism Squad, Hemant Karkare, was one of at least 11 security personnel killed in the shootouts.
Another siege was in progress at Nariman House, an office building that houses a Jewish centre. The chairman of the Indian Jewish