Mumbai police spokesman Satish Katsa said gunmen have taken over the Taj Mahal Hotel and Hotel Oberoi, and were holding hostages on multiple floors.
Flames and smoke poured from the Taj early Thursday, and several explosions were heard at the building.
At the Oberoi the military reportedly entered the building and a large explosion was heard shortly afterwards.
Another hostage situation was unfolding at Cama Hospital, CNN's sister network in India, CNN-IBN reported.
Earlier, A.N. Roy, the police chief of Maharashtra state, said there were ongoing battles at the two five-star hotels.
One witness told local reporters that gunmen tried to find people with U.S. or British passports and took about 15 of them hostage.
Andrew Stevens, a CNN anchor who was staying at the Taj with a CNN crew, estimated about half the hotel's guests were Westerners.
British businessman Alan Jones told CNN.com how he was about to get out of an elevator in the Oberoi when another guest was shot.
"A bullet hit one of the Japanese men in the back of the leg. Flesh and blood splattered everywhere."
IBN, quoting police sources, reported hostages were taken at the both hotels.
Gunmen armed with automatic weapons and grenades hit nine sites including the hotels, a cafe, a hospital and a train station in coordinated attacks, police say.
Maharashtra state government spokesman Bhushan Gagrani said 78 people were killed and about 200 wounded, while police confirmed 26 deaths.
Among the dead is the head of the Maharashtra state's anti-terror squad, who apparently died in the violent aftermath of the attacks rather than being a target for the killers.
Two suspected militants were gunned down and nine suspects had been arrested, Gagrani said. Three people were detained for questioning from one of the hotels, he added.
Sajjad Karim, associated with a group of European lawmakers attending an upcoming EU-India summit, told The Associated Press that he was in the main lobby of the Taj Mahal Hotel when "there was all of a sudden a lot of firing outside."
As he tried to get away, he told the AP: "Another gunmen appeared in front of us, carrying machine gun-type weapons. And he just started firing at us. ... I just turned and ran in the opposite direction."
Video showed scenes of chaos, with people crowding Mumbai's streets, some helping others who appeared to be wounded.
The attacks began about 2230 local time (1700 GMT) and more than two hours later witnesses were reporting new explosions and gunfire.
A group called Deccan Mujahideen claimed responsibility, IBN reported, but analysts told CNN that may be a front name to throw investigators off who was really behind the attacks.
The targets include businesses frequented by international visitors in the city which is India's financial center.
A local journalist told CNN he had seen evidence of an attack at the city's domestic airport, which is on the outskirts of the Mumbai.
IBN reported explosions at a gas station and inside a taxi on a dockside road.
Attacks were carried out at the Taj and Oberoi hotels, the popular Café Leopold, and Cama Hospital, and the Chhatrapati Shivaji Terminus railway station.
Sourav Mishra, a Reuters.com reporter, was with friends at the Cafe Leopold when gunmen opened fire.
"I heard some gunshots ... 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.
India has suffered a number of attacks in recent years, including a string of bombs that ripped through packed Mumbai commuter trains and platforms during rush hour in July 2006. About 209 people were killed in that attack.
Last July, a series of synchronized bomb blasts in the western Indian city of Ahmedabad left 49 dead and more than 100 wounded, police said.
But Paresh Parihar, a businessman in Mumbai, described Wednesday's attacks as unlike anything he had seen.
"They really don't fear for their lives or any other activity that could put them in danger," he told CNN. "This is really a very unusual situation."
U.S. State Department spokesman Robert Wood said: "We are monitoring the situation very closely and stand ready to support the Indian authorities as they deal with this horrific series of attacks."
The U.S. has opened a telephone hotline for citizens concerned about family or friends who may be visiting or living Mumbai.