Maharashtra state police said that commandoes had freed hostages from the Taj Mahal hotel, but that people are still being held in the nearby Oberoi hotel and the orthodox Jewish Chabad Lubavitch center.
India's prime minister has blamed outside forces on the attacks.
"It is evident that the group which carried out these attacks, based outside the country, had come with single-minded determination to create havoc in the financial capital of the country," Manmohan Singh told national TV.
Eyewitnesses have reported several explosions at the Oberoi hotel, where a special police unit has begun an operation to free the hostages. Maharashtra official Bhushan Gagrani said all the hostages would be free by this evening, but did not say how many are being held.
The buildings were seized by gunmen after a series of shootings late on Wednesday in Mumbai's tourist and business district, targeting popular restaurants, a cinema, a hospital, a backpackers' pub, and a train station. Mumbai police said as of Thursday afternoon at least 101 people were dead, and 314 injured.
At least six foreign nationals have been killed, including an Italian, a Japanese man, and an Australian.
A previously unknown Islamist group calling itself the Deccan Mujahideen has claimed responsibility for the attacks.
Hostages who escaped from the hotels described the militants as young men speaking Hindi or Urdu, and said they had attempted to round up all the British and American guests.
The militants are believed to have arrived in Mumbai by boat near the Gate of India, before spreading out around the city center, armed with assault rifles and hand grenades, and launching their attacks.
The home secretary of Maharashtra state, Bipin Shrimali, said four militants had been shot dead as they fled in cars, and another four had been killed by special police in the Taj Mahal hotel. Police said nine other suspects had been arrested.
