The suspect, Mehare Alam, who was arrested in Bihar's Darbhanga district on Wednesday, was being brought to Patna by the NIA.
He was in the custody of the NIA and the Muzaffarpur Police when he escaped on Wednesday night, reports said.
When the team stopped in the city of Muzaffarpur, Alam reportedly said he wanted to use the toilet and slipped away.
After the escape, the NIA lodged an FIR with the town police station. A search has been mounted by the NIA.
The agency on Thursday said it has arrested a fourth suspect in connection with the serial blasts.
The NIA arrested the fourth suspect, who was identified as Uzair Ahmed, from Jharkhand's Ranchi city on Wednesday.
The Bihar Police on Wednesday said they have arrested the third suspect in the serial blasts. The arrested suspect was identified as Tabish.
Based on leads provided by Imtiaz Ansari, who was arrested in connection with the blasts, the police picked up Tabish from Motihari in Bihar.
Ansari is one of the six men named in the FIR that also names his mentor Tehseen Akhtar, reports said.
The escaped suspect was reportedly close Akhtar.
The police said that Ansari could be part of a newly formed module of the terror group Indian Mujahideen in Ranchi set up by Akhtar and wanted to create panic and trigger a stampede that could cause many deaths.
Six people were killed and over 80 others were injured in a series of crude bomb explosions before Modi's Hunkar Rally at Gandhi Maidan in Patna.
--IBNS (Posted on 31-10-2013)