Roy said efforts were continuing to free hostages held at the Trident Oberoi.
"That is why the operation is being conducted more sensitively to ensure there are no casualties of innocent people," he said.
The standoff on Thursday at the hotels came after the armed men, suspected to number about 100, staged attacks on several high-profile targets across India's financial capital.
Police say six attackers have been killed and nine others arrested since the violence began late on Wednesday.
Besides the two well-known hotels, the heavily-armed attackers targeted a restaurant, a hospital and a railway station, among others.
"We're going to catch them dead or alive," R R Patil, home minister for Maharashtra state, told reporters. "An attack on Mumbai is an attack on the rest of the country."
At least nine foreign nationals are among the dead, police have said, while funerals are being held for police officers killed during the attacks.
Manmohan Singh, India's prime minister, said that the attackers were likely to have received assistance outside the country.
"I strongly condemn these senseless acts of violence against innocent people, including guests from foreign countries," he said.
"The well-planned and well-orchestrated attacks, probably with external linkages, were intended to create a sense of terror by choosing high-profile targets.
"It is evident that the group that carried these attacks, based outside the country, had come with single-minded determination to create havoc in the commercial capital of the country."
Reports say that the attackers had landed on the shores of Mumbai on an inflatable boat, before heading towards their intended targets.
"They told everybody to stop and put their hands up and asked if there were any British or Americans … My friend said to me, 'don't be a hero, don't say you are British.'"
- Alex Chamberlain, British guest at the Oberoi Trident who fled via a fire escape
"That was, without doubt, the worst experience of my entire life … We could hear the army coming through the hotel ... The firemen broke the windows of the room and we climbed down the ladder."
- Female guest, Taj Mahal hotel
"They wore black T-shirts and blue jeans. They were carrying big guns … They just fired randomly at people and then ran away. In seconds, people fell to the ground."
- Nasim Inam, at Chhatrapati Shivaji railway terminus
"As I stepped inside the lobby gunshots started to go off ... There were people getting shot in the corridor. There was someone dead outside the bathroom."
- Brooke Satchwell, an Australian television actress, who hid in a cupboard in the Taj Mahal hotel
"We had literally just ordered and then it seemed like firecrackers – people were screaming … I turned around and she was crawling out the door because she couldn't walk."
- David Coker, an Australian student, who was shot along with his girlfriend at the Cafe Leopold restaurant
Witnesses at the targeted hotels said the attackers singled out British and American citizens.
"They kept shouting: 'Who has US or UK passports?'" Ashok Patel, a British citizen who fled from the Taj Mahal hotel, said.
Several European legislators, visiting Mumbai ahead of a European Union-India summit, were among those inside the Taj when it was besieged.
Indian police said eight locations were targeted in what they called terrorist attacks.
In addition to the Taj and Trident hotels, the historic Chhatrapati Shivaji train station, Leopold Cafe and the police headquarters in southern Mumbai were hit.
The attackers also stormed the Mumbai headquarters of Chabad Lubavitch, an Orthodox Jewish outreach group, where a rabbi and his family were staying.
The rabbi was identified as Gabriel Holzberg, the Israeli rescue service Zaka said.
Holzberg's wife and a two-year-old child were later freed, after Indian commandos entered the Chabad building, Zaka said.
But unconfirmed reports say that Rabbi Holzberg had been injured.
"The situation at the present moment is very unclear. We know there is a hostage situation at the Chabad centre and also in one of the hotels in town," Yigal Palmore, an Israeli foreign ministry spokesman, said.
'Shock' at attacks
Al Jazeera's Riz Khan, reporting from Mumbai, said the targeted buildings are popular not only with tourists but local elites as well.
They were clearly chosen by the attackers to give their assaults maximum exposure, he said.
Shai Venkatraman, a correspondent with the private New Delhi Television channel, said that Mumbai was in a state of shock following the co-ordinated attacks.
"Mumbai is not new to terror but this has really shocked people. There is a stunned silence," she told Al Jazeera.
"This has really damaged Mumbai's reputation, even though it is a city that is usually quick to come back.
"This time, the attack has really shaken the people."
Group claims attacks
A little known group calling itself the Deccan Mujahedeen claimed responsibility for the attack in emails to news organisations, but Mahan Abedin, an insurgency analyst, told Al Jazeera he had never heard of the group.
|The co-ordinated attacks are the most severe to have hit Mumbai in months [AFP]
"At this stage, that name does not necessarily mean that much," he said.
"It is very tempting to point the finger at Muslim militants, and indeed they have been the main culprits in the pattern of attacks", Abedin said, but cautioned that "one has to be careful before pointing the finger".
"We have seen an increase in recent years in indigenous Indian Muslim organisations beginning to take a violent stance towards the Indian state and sections of the Indian society, particularly the commercial elite of places like Mumbai, in order to highlight, they would say, the sheer inequality of life in India.
"There is a middle class of around 100 million who live very well but 800 million-plus people live in miserable conditions," he said.
Anti-terror chief killed
At least three senior Indian police officers, including Hemant Karkare, the chief of the city's anti-terrorism squad, were among those killed, police official A N Roy said.
Maharashtra's chief minister said 11 police officers were killed in all.
The motive for the attacks was not immediately clear, but India has witnessed a series of co-ordinated attacks in recent months.
A little-known group called the Islamic Security Force-Indian Mujahedeen, claimed responsibility for a series of blasts last month in which 80 people died in the northeast state of Assam.
A total of 12 explosions shook the northeastern state, six of them ripping through crowded areas in the main city of Guwahati.
Six weeks earlier, the capital New Delhi was hit by a series of bombs in crowded markets that left more than 20 people dead.
Those attacks were claimed by a group calling itself the Indian Mujahedeen.