Troops began moving into one of the hotels, the Oberoi, local television said. Explosions were heard there and at the Taj Mahal hotel, where tourists were also said to have been taken hostage, CNN/IBN television reported.
Police said at least 250 people were wounded in the series of Mumbai attacks which, apart from the hotels, targeted hospitals and railway stations as well as the Cafe Leopold, perhaps the most famous restaurant and hang-out for tourists in the city.
An organisation calling itself the Deccan Mujahideen claimed it was behind attacks, television channels said. The previously little known group sent an email to news organisations claiming responsibility.
"I guess they were after foreigners, because they were asking for British or American passports," said Rakesh Patel, a British witness who lives in Hong Kong and was staying at the Taj Mahal hotel on business. "They had bombs."
"They came from the restaurant and took us up the stairs," he told the NDTV news channel, smoke stains all over his face. "Young boys, maybe 20 years old, 25 years old. They had two guns."
India has suffered a wave of bomb attacks in recent years. Most have been blamed on Islamist militants, although police have also arrested suspected Hindu extremists thought to be behind some of the attacks.
No one has claimed responsibility for the latest Mumbai attacks.
Hemant Karkare, the chief of the police anti-terrorist squad in Mumbai, was killed during the attacks, police said.
In Washington, the White House condemned the attacks. France, current president of the European Union, also condemned the attacks and hostage-takings.
A European official was among the wounded.
"My hotel is surrounded by police and there are gunmen inside," European lawmaker Ignasi Guardans told Spanish radio from the Taj. "We are in contact with some deputies inside the hotel, with one in a room and another hidden in the kitchen. There's another official hurt and in hospital."
Home Minister Shivraj Patil said there were around four or five attackers in each of the two hotels.
"They have attacked hotels, they have attacked the hospitals, they have attacked the railway station," he said, adding that two attackers had been killed and two arrested.
KOREANS AND EUROPEANS CAUGHT UP IN ATTACKS
A driver told Reuters at least 50 Koreans were stuck inside the Taj with their drivers waiting outside.
"We were just getting ready to pick them up, when we heard the first blast, police did not let us get past and they (the Koreans) are not answering the phones," Deepak Aswar, the driver said. Europeans were also caught up in the attacks.
"I was in the restaurant inside Oberoi and I saw this series of gunshots and death which I don't want to see again," a Spaniard who declined to give his name told Reuters.
"I crawled out into the kitchen and waited there, until I sensed it was all quiet and seemed over."
Maharashtra state police chief A.N. Roy said attackers had fired automatic weapons indiscriminately, and used grenades, adding that they were still holed up in some buildings.
Sourav Mishra, a Reuters reporter, was with friends at the Cafe Leopold when gunmen opened fire around 9:30 p.m. He has received injuries and is in St. George's Hospital.
"I heard some gunshots around 9:30. I was with my friends. Something hit me. I ran away and fell on the road. Then somebody picked me up. I have injuries below my shoulder," Mishra said from a hospital bed he was sharing with three other people.
Another Reuters reporter saw a hospital ward full of injured people with bullet and shrapnel wounds. Many people were crying as the injured were brought in on trolleys.