"An attack on Mumbai is an attack on the rest of the country."
Six foreigners are among the dead, police have said.
By dawn on Thursday Indian army troops called in to support the police had begun moving into the two hotels and there were reports of gun battles.
Pollice loudspeakers have announced a curfew around the areas where the attacks have taken place.
Authorities have said that the attackers had first made their way to the Taj hotel on an inflatable boat.
"We have been told that there were 12 people [on the boat]; they split up into smaller groups and then went off to the various locations were the attacks took place," James Wright, reporting for Al Jazeera, said.
Indian authorities said several foreigners were thought to be held hostage at the Taj Mahal hotel, but it was not immediately clear if hostages at the Oberoi were Indians or foreigners, said Anees Ahmed, a senior state official.
Witnesses at both hotels said the attackers singled out British and American citizens.
"They kept shouting: 'Who has US or UK passports?'" said Ashok Patel, a British citizen who fled from the Taj Mahal.
Several European legislators, visiting Mumbai ahead of a European Union-India summit, are reportedly among those who have barricaded themselves inside the hotel.
It was also unclear where the hostages were in the Taj Mahal, which is divided into an older wing, part of which was in flames, and a modern tower that was not on fire.
Indian police, said eight locations were targeted in what they called terrorist attacks, including the two hotels.
Other hotels, the crowded Chhatrapati Shivaji train station, Leopold's restaurant, and the police headquarters in southern Mumbai have also been hit.
A Jewish rabbi and his family are also thought to be under threat after gunmen stormed the building in which they were staying.
"The name of the place is Chabad house in South Mumbai. I hear commandos are storming the apartment block, which is a four-storey building," Jonathan Solomon, the chairman of the Indian Jewish Federation, said.
"A rabbi is in there with his family ... I do not know the number of gunmen in there. I don't know how many family members are in there."
'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, and were clearly chosen by the attackers to give their assaults maximum exposure.
|A popular restaurant, a busy railway station and a police station were also hit [AFP]
Shai Venkatraman, a correspondent with the private New Delhi Television channel, said that Mumbai was in a shock 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. But this time, the attack has really shaken the people.
"The situation at the Taj hotel is especially bad. There are reports that there are about four terrorists there and we are hearing that about 20 to 25 people are trapped at the hotel.
"There are no negotiations going on. At the moment, there are just exchanges of gunfire."
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.
"At this stage, that name does not necessarily mean that much," he said.
Abedin 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", 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 AN Roy said.
|The co-ordinated attacks are the most severe to have hit Mumbai in months [AFP]
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.