The near-simultaneous explosions were reported in Uttar Pradesh's capital of Lucknow and nearby towns of Faizabad and Varanasi, one of the holiest cities for Hindus because the Ganges River flows through the city.
Various reports said the blasts occurred within minutes of one another near local courts.
The Press Trust of India reported at least 10 people were killed in the blasts, all in Faizabad and Varanasi, while an unknown number of injuries were reported in Lucknow.
Uttar Pradesh is India's largest state and the constituency of Sonia Gandhi and her son Rahul Gandhi of the Congress Party, which leads India's ruling coalition. Uttar Pradesh itself is ruled by an opposition party.
The PTI report said the blasts come a week after Uttar Pradesh and federal security agencies foiled an alleged plot by arresting three members reportedly belonging to the terrorist group Jaish-e-Mohammed, which is based in Pakistan. Earlier reports had said the three had allegedly planned to abduct a prominent political person, which some said claimed was to be Rahul Gandhi.