Police killed at least two of the terrorists and have launched a commando operation at the Oberoi hotel, according to the Times of India.
Firing was also reported near the Maharashtra State Assembly building in South Mumbai.
Prime Minister Manmohan Singh has condemned the attacks in Mumbai and pledged the Maharashtra state government his full assistance.
Commandos were on standby and the national disaster response force unit is being rushed to Mumbai, the ministry of home affairs officials said.
The U.S. State Department condemned the attacks "in the strongest terms" and is working to issue a warden statement notifying Americans in the area. The department has not yet confirmed if any Americans were killed, wounded or taken hostage.
"Secretary[Condoleezza] Rice has been briefed on the attacks in Mumbai and is monitoring the situation closely. The Secretary will be reaching out to officials at the US Embassy in New Delhi and at the consulate in Mumbai. She will be reaching to Indian government officials as well. The situation on the ground is extremely fluid," a State Department official told ABC News.
President-Elect Barack Obama also criticized the attacks, saying "we stand with the people of India."
"President-Elect Obama strongly condemns today's terrorist attacks in Mumbai, and his thoughts and prayers are with the victims, their families, and the people of India," said Brooke Anderson, Obama's transition national security spokesperson. "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," she said
The Associated Press contributed to this report. Additional reporting by ABC News' Karen Russo in New Dehli as well as Kirit Radia and Pierre Thomas in Washington DC.