Federal Home Minister Sushilkumar Shinde said the bombs were attached to two bicycles about 150 meters (500 feet) apart in Dilsukh Nagar, a residential and commercial district. He said eight people died in one explosion and three in the other. He spoke to reporters in New Delhi, the Indian capital.
The blasts occurred about two minutes apart outside a movie theater and a bus station, police said.
"This is a dastardly attack, the guilty will not go unpunished," Prime Minister Manmohan Singh said. He appealed to the public to remain calm.
Television images showed the injured being taken to nearby hospitals.
The last major bomb attack in India was a September 2011 blast outside the high court in New Delhi that killed 13 people.
Federal Home Secretary R.K. Singh said officials from the National Investigation Agency and commandos of the National Security Guards were leaving New Delhi for Hyderabad, the capital of Andhra Pradesh.
India has been in a state of alert since Mohammed Afzal Guru, a Kashmiri, was hanged in a New Delhi jail nearly two weeks ago. Guru had been convicted of involvement in a 2001 attack on India's Parliament that killed 14 people including five gunmen.
Many in Indian-ruled Kashmir believe Guru did not receive a fair trial, and the secrecy with which the execution was carried out fueled anger in a region where anti-India sentiment runs deep.
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