Union Home Secretary Anil Goswami said six explosions occurred in and around the rally site, where tens of thousands of people gathered, Press Trust of India reported.
A doctor at an area hospital said eight of the nearly 70 people injured were in "very critical condition," the Indo-Asian News Service reported.
Hours before the multiple blasts police said a bomb detonated in a toilet at the Patna railway station, not far from the rally. During a sweep after the explosion, bomb disposal units found two more bombs, Railway Superintendent of Police Upendra Kumar Sinha said.
At the rally, smoke could be seen rising from two of the bomb sites as Bharatiya Janata Party leaders addressed the crowd.
Prime Minister Manmohan Singh condemned the blasts and appealed for calm.
PTI reported the Home Ministry has asked for a report on the incident from the Bihar state government and sent teams from the National Investigation Agency and the National Security Guard to investigate.