A.N. Roy, a senior police officer, saidpolice were battling the gunmen.
"The terrorists have used automatic weapons and in some places grenades have been lobbed. The encounters are still going on and we are trying to overpower them," Roy said.
The gunmen attacked two luxury hotels, the Taj and the Oberoi, as well as the Chhatrapati Shivaji Terminus station in southern Mumbai and Leopold's restaurant, a Mumbai landmark.
Television stations showed fires in the lobby of both hotels and people being evacuated from the Oberoi with their hands on their heads.
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.
A British Euro-MP was among guests under siege in their Mumbai hotel in the wake of the attacks.
Sajjad Karim, speaking by mobile phone from a barricaded basement room at the Taj Mahal Palace hotel, said he and others had fled from machine-gun fire and had no idea why the hotel was targeted.
He said: "I was in the lobby of the hotel when gunmen came in and people started running. There were about 25 or 30 of us.
"Some of us split one way and some another. A gunman just stood there spraying bullets around, right next to me. I managed to turn away and I ran into the hotel kitchen and then we were shunted into a restaurant in the basement.
"We are now in the dark in this room and we've barricaded all the doors. It's really bad."
Mr Karim is part of a delegation of Euro-MPs visiting Mumbai ahead of the forthcoming EU-India summit.
He said that as he ran from the lobby, he saw people falling but did not know the extent of any casualties. He said it seemed to be a "random attack".
Mr Karim, a North West MEP, defected from the Liberal Democrats to the Conservatives in the European Parliament a year ago.
The Taj Mahal Palace, one of the most famous hotels in India, was home to the England cricket team when they visited Mumbai around two weeks ago.
They were also planning to use the hotel on their return to the city for the team's second Test Match against India, which is scheduled to start on 19 December.
The team were in the eastern Indian city of Cuttack today after losing their latest one-day game against India.
