Farooq Takla, who was absconding since 1995, had applied for renewal of his passport from Dubai on February 7, 2011 and the document was renewed the next day despite a Red Corner Notice against him.
At that time, P Chidambaram was the Union Home Minister and SM Krishna was serving as the Minister of External Affairs.
Calling it as a major lapse on the part of the then External Affairs Ministry, the BJP attacked the Congress and demanded a probe in the matter.
"How come his passport was renewed within a day without conducting a proper investigation. It's a serious issue and should be probed thoroughly," BJP MP Meenakshi Lekhi said.
The Congress also asked for a probe but said its ministers had no role in Farooq's passport renewal because these applications generally don't reach the ministers but remain limited to passport officials.
Farooq (57) had fled from India after the 1993 blasts in Mumbai and a Red Corner Notice was issued against him in 1995.
He was arrested by the CBI on Thursday at the Indira Gandhi International Airport in Delhi after being deported from Dubai.
Farooq was deported from the UAE with the help of central intelligence agencies and put on a flight to Delhi.
He faces criminal conspiracy, murder, attempt to murder, voluntarily causing hurt by dangerous weapons or means and several other charges.
Farooq is considered as a close aide of Dawood Ibrahim, the key accused in the case of 1993 Mumbai serial blasts that left nearly 257 people dead, 713 seriously injured.
On March 12, 1993 the country's commercial capital witnessed an unprecedented terrorist attack when a series 12 bomb explosions took place one after another in about a span of two hours.
The dastardly attacks destroyed properties worth Rs 27 crore.