The Prime Minister phoned chief minister Nitish Kumar and asked him to ensure a speedy investigation. The security lapse is a major ignominy for the chief minister, who ended his party's alliance with the BJP in August over its decision to give Mr Modi the starring role in its campaign for the national election.
There was chaos for a few minutes after five blasts took place within 10 minutes at Gandhi Maidan, one of them near the main entrance. TV cameras showed smoke billowing and the police dragging away a man for interrogation. (Caught on camera: bomb explodes at Modi's rally venue in Patna)
By the time Mr Modi was ready to address the crowd, people had settled down; many were seen waving BJP flags.
The first bomb exploded around 11 am at the railway station in Patna, killing one person and injuring another. Two other bombs were defused there, said police officers. (Reactions to the blasts)
Mr Kumar who depends heavily on the support of Bihar's Muslims, sought to distance himself from Mr Modi after the 2002 communal riots in Gujarat, in which over a thousand people were killed, most of them Muslims.
In June this year, Mr Kumar ended his partnership with the BJP when it became clear, he said, that the party would pick Mr Modi as its candidate for prime minister, which it did three months later.