Major-General Qassim Atta, a spokesman for the military's Baghdad operations, said that Ibrahim was the primary culprit responsible for the attack.
Ibrahim said that he was a police chief in Diyala province, northeast Iraq, under Saddam until 1995 and then worked as a lawyer until 2002, after which he became a leading Ba'athist official in the same province.
The second bombing on Wednesday occurred minutes later at the ministry of foreign affairs.
The tape was released amid significant political concern over how the trucks were able to enter central Baghdad and reach government institutions.
|The attacks near and in the Green Zone killed
at least 95 people [AFP]
They were the deadliest attacks since US forces pulled out of urban centres at the end of June.
Jane Arraf, correspondent for the Christian Science Monitor in Baghdad, told Al Jazeera the bombings have exposed the deep divisions still threatening the country's political system.
"The Baghdad governor told me last night that he believed that Sunni members of parliament were responsible and then he cast the blame wider, saying that neighbouring countries were funding this, specifically, he said Saudi Arabia.
"This points to the big divide between the Sunni and the Shias. At the top levels it is still very bitter."
The removal of "T-walls" - blast-proof concrete security walls - in Baghdad has been stopped as safety fears have grown.
"We will re-examine our strategy on security matters," Salah Abdul Razzaq, Baghdad's governor, said.
He said the assailants had exploited citizens' desire to see the concrete barriers removed, which in turn made it easier to conduct the attacks.
Officials said that more than 10 people had been arrested, comprising the complete network concerning the attacks.
Officials fear the bombings may further undermine public confidence in the ability of Iraqi security forces to keep control following plans for US forces to completely withdraw by the end of 2011.