Witnesses said civilians could be seen running from the hotel, some with suitcases. Ambulances were also reported to be arriving.
But the BBC's Mark Dummett, outside the Taj Mahal, says the situation has since become very confused, with the sounds of explosions and gunfire being heard from within the hotel, suggesting the siege is not yet over.
Earlier in the day, Indian commandos had been seen entering the hotels but there was little detail on the operation.
Mr Roy said some people were still apparently being held hostage at the Oberoi. "That is why the operation is being conducted more sensitively to ensure there are no casualties of innocent people," he said.
Meanwhile, explosions have been heard outside a Jewish centre in the city, where an Israeli rabbi is believed to be one of a number of hostages being held there.
"We all moved through the lobby in the opposite direction and another gunman then appeared towards where we were moving and he started firing immediately in our direction."
One British tourist had been holed up in his room at the Oberoi hotel throughout the night, hearing sporadic gunfire, small explosions and people running up and down the corridor.
"I've barricaded my room, I'm keeping my head down," he told the BBC.
Other tourists told of groups of 20 to 30 people to a room, lying on the floor and staying very quiet.
Most of the attacks have been blamed on Muslim militants, although police have also arrested suspected Hindu extremists.
The BBC's Sanjeev Srivastava says the timing and symbolism of the latest attacks could not have been worse.
By choosing to target the richest district of India's financial capital in such a brazen and effective manner, he says those behind the attacks have perhaps dealt the severest blow to date to the morale and self esteem of the Indian authorities.
The attacks have come amidst elections in several Indian states and exposes the governing coalition to the charge that it has failed to combat terror, our correspondent says.
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