Officials say police have killed four suspects and arrested nine more. State home secretary Bipin Shrimali says four men were killed in two incidents when they tried to flee in cars. State Home Minister R.R. Patil says 9 others were arrested, but declines to provide details.
Johnny Joseph, chief secretary for Maharashtra state, said the death toll could rise further.
The gunmen attacked the Chhatrapati Shivaji Terminus station in southern Mumbai and Leopold's restaurant, a Mumbai landmark. Police reported hostages being held at the Taj Mahal and Oberoi hotels, two of the best-known upscale destinations in this crowded but wealthy city.
A media report says the little-known Deccan Mujahideen group has claimed responsibility for the terrorist attacks. The Press Trust of India news agency said the group sent e-mails to several media outlets.
Television channels reported that Westerners were being held hostage at two five-star hotels. The U.S. government is "assessing the hostage situation," the White House said Wednesday.
"No word on any American casualties at this point, and still assessing the hostage situation," said Ben Chang, a spokesman for the White House National Security Council, when asked whether an Americans were being held after attacks apparently aimed at tourists, Reuters reported.
Maharashtra state police chief A.N. Roy said attackers had fired automatic weapons indiscriminately, and used grenades.
"These are terrorist strikes in at least seven places," he told the NDTV news channel.
An explosion followed by a raging fire struck one of the hotels. Large plumes of smoke were seen rising from the top of the landmark Taj early Thursday. Screams could be heard from the century-old edifice on Mumbai's waterfront. Firefighters were spraying water at the blaze.
Authorities believed seven to 15 foreigners were prisoners at the Taj, but it was not immediately clear if hostages at the Oberoi were Indians or foreigners, said Anees Ahmed, a top state official.
The attackers specifically targeted Britons and Americans, witnesses said. Fires burned and gunfire was heard for hours.
Gunmen who burst into the Taj "were targeting foreigners. They kept shouting: `Who has U.S. or U.K. passports?"' said Ashok Patel, a British citizen who fled from the hotel.
Bhisham Mansukhani, a journalist, was attending a wedding reception at the Taj's Crystal Room. "I was inside the bar when glass shards almost hit my eye," he told the Times of India.
Rakesh Patel, a British witness who lives in Hong Kong and was staying at the Taj hotel on business said the bomb-wielding attackers appeared to be after foreigners because they asked for people with British or American passports.
"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."
An eyewitness told the BBC he saw a gunman opening fire in the lobby of Taj Mahal hotel. He said he saw people fall before he fled the lobby.
"All I saw was one man on foot carrying a machine gun type of weapon -- which I then saw him firing from and I saw people hitting the floor, people right next to me," he said.
Alex Chamberlain said a gunman, a young man of 22 or 23, ushered 30 or 40 people from the restaurant into a stairway and ordered everyone to put up their hands. He said the gunman spoke in Hindi or Urdu.
"They were talking about British and Americans specifically. There was an Italian guy, who, you know, they said: 'Where are you from?" and he said he's from Italy and they said 'fine' and they left him alone. And I thought: 'Fine, they're going to shoot me if they ask me anything -- and thank God they didn't," he said.
Chamberlain said he managed to slip away as the patrons were forced to walk up stairs, but he thought much of the group was being held hostage.
Sourav Mishra, a Reuters reporter, was with friends at the Cafe Leopold when gunmen opened fire around 9:30 p.m.
"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.
Leopold's restaurant was riddled with bullet holes and there were blood stains on the floor and shoes left by fleeing customers, according to an Associated Press reporter at the scene.
State Department spokesman Robert Wood said the United States "strongly condemns the terrorist attacks that have taken place in Mumbai, India. We are monitoring the situation very closely and stand ready to support the Indian authorities as they deal with this horrific set of attacks."
Mumbai has been hit repeatedly by terror attacks since March 1993, when Muslim underworld figures tied to Pakistani militants allegedly carried out a series of bombings on Mumbai's stock exchange, trains, hotels and gas stations. Authorities say those attacks, which killed 257 people and wounded more than 1,100, were carried out to revenge the deaths of hundreds of Muslims in religious riots which had swept India.
A decade later in 2003, 52 people were killed in Mumbai bombings blamed on Muslim militants and in July 2007 a series of seven blasts ripped through railway trains and commuter rail stations. At least 187 died in those attacks.
Relations between Hindus, who make up more than 80 percent of India's 1 billion population, and Muslims, who make up about 14 percent, have sporadically erupted into bouts of sectarian violence since British-ruled India was split into independent India and Pakistan in 1947.
Many world leaders and President-elect Barack Obama issued statements condemning the attacks.
"These coordinated attacks on innocent civilians demonstrate the grave and urgent threat of terrorism. The United States must continue to strengthen our partnerships with India and nations around the world to root out and destroy terrorist networks. We stand with the people of India, whose democracy will prove far more resilient than the hateful ideology that led to these attacks," said Brooke Anderson, Mr. Obama's chief national security spokesperson.