The attacks happened on Tuesday evening in a packed railway station and crowded temple in Hinduism's holiest city, Varanasi, raising fears of communal violence between majority Hindus and minority Muslims.
The first bomb went off in the packed Sankat Mochan temple where hundreds of devotees of the Hindu deity Hanuman had gathered for evening prayers.
The second exploded at the city's cantonment railway station. Police had said on Tuesday that two bombs exploded at the station.
A mob of Hindus briefly blocked the motorcade of Mulayam Singh Yadav, the chief minister of Uttar Pradesh state, when he visited the scene.
Yadav, whose party champions the cause of Muslims and lower-caste Hindus, inspected the site under heavy protection while people shouted slogans against him.
Varanasi, meanwhile, was largely shut down by a strike called by Hindu nationalist groups to protest against the bombings. Markets were closed and vehicles kept off the roads. The authorities also ordered that schools be closed because of the strike call.
But there was no sign of wider violence in reaction to the attack.
Yashpal Singh, the police chief of Uttar Pradesh state, where Varanasi is located, said he suspected the hand of Pakistan-based group, Lashkar-e-Taiba.
Vigil at temples
Indian TV channels said two Lashkar fighters were shot dead overnight by police in New Delhi and another Lashkar man was killed in Lucknow, Uttar Pradesh's capital, but it was not known if they were connected to the Varanasi blasts.
Armed police mounted vigils at temples and public places across India and the authorities said they had shut down schools and colleges as a precaution, but a Reuters reporter said traffic on the streets of the ancient city appeared normal.
Prem Lata, a 65-year-old housewife, said: "People are moving around. Puja (worship) is going on in the temples. There is no problem now."
Temple-studded Varanasi, 670km southeast of the capital New Delhi, is on the banks of the Ganges river, considered holy by Hindus.
Hindus believe that dying in Varanasi, being cremated on the banks of the Ganges and the ashes immersed in the river ensures release from the cycle of rebirth. Many elderly and ill people come to the city if they believe they are close to death.