The BBC is reporting western hostages are being held captive at Mumbai's top luxury hotel the Taj Hotel.
The Times of India, India's leading online newspaper, reports at least 80 people are dead after a series of co-ordinated attacks by terrorist gunmen at seven sites in Mumbai, including two luxury hotels and other popular tourist locations.
At least 250 are reported injured.
A British witness has told Indian TV the attackers wanted anyone with a British or American passport.
Indian police said gunmen attacked two luxury hotels, the Chhatrapati Shivaji Terminus station in southern Mumbai and Leopold's restaurant, a Mumbai landmark.
Another luxury hotel, Oberoi Hotel, is on fire following the attacks.
The gunmen, some also armed with grenades, attacked targets including the hotels, a cafe, and a train station, police say.
The Times of India reports the terrorists hijacked a white police jeep near Metro cinema in South Mumbai.
Firing was also reported near Maharashtra state assembly building in South Mumbai.
A.N. Roy, a senior police officer, said police were battling the gunmen.
The targets include businesses frequented by international visitors.
"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.
"It seems to be a terrorist attack, many places under siege by gunmen," A.K. Sharma, a Mumbai government railway police commissioner, told local television.
The Associated Press reported that police said gunmen had attacked the Chhatrapati Shivaji Terminus station in southern Mumbai and Leopold's restaurant, a Mumbai landmark. A reporter at the restaurant says it is pitted with bullet holes and blood stains on the floor.