City police spokesman Rajan Bhagat told reporters that in addition to the fatalities, at least 97 people were injured.
At least five blasts went off in quick succession in crowded areas of the city, including one at the India Gate, a major cultural site.
An Islamic group named the Indian Mujahideen sent an e-mail to Indian media outlets claiming responsibility for the attacks. The group had also claimed responsibility for terrorist blasts in Jaipur in May and Gujarat in June, in which a total of 106 people died.
"In the name of Allah, Indian Mujahideen strikes back once more," the message said.
Police commandos have carried out raids across the city, and arrested several suspects.
The police spokesman said "vital evidence" had been gathered and that investigators hope to solve the case soon.