Blagojevich will face a retrial in April on 23 charges, including allegations he sought to sell or trade an appointment to Obama's seat. At his first trial, jurors deadlocked on all but one count of lying to the FBI.
The motion contends Blagojevich's multiple references to Madigan in the recordings counter government assertions that talk of a Madigan deal was merely a ruse to obscure other bids by Blagojevich to profit personally.
The seven-page motion, filed in the U.S. District Court in Chicago, says Blagojevich is heard in the excerpts discussing the idea of appointing Madigan in exchange for her father, Illinois House Speaker Michael Madigan, pushing a legislative package favored by then-Gov. Blagojevich.
"The calls that form the basis of this motion demonstrate a more complete picture of the Governor's state of mind with regard to the Madigan appointment and contradict the government's theory," the motion says.
A spokeswoman for the U.S. attorney's office in Chicago, Kim Nerheim, declined to comment on Monday's motion.
A 34-page motion filed last Tuesday by Blagojevich similarly attempted to bolster the contention that a Madigan deal was being seriously considered on the very eve of his arrest.
The two motions come in advance of a Feb. 15 deadline set by presiding Judge James Zagel for filing pre-trial motions.
Last week's motion says a record of a phone call between a top Blagojevich aide and Rahm Emanuel -- then designated Obama's White House chief of staff -- is among allegedly missing evidence. It asks Zagel to order prosecutors to turn over records of the call, saying it would strengthen the former governor's claim of innocence.
The call allegedly took place just a day before Blagojevich's Dec. 9, 2008, arrest. His attorneys argue the conversation could support a contention that Emanuel, who has not been accused of any wrongdoing, was willing to help broker the alleged political deal that could have led Blagojevich to appointing Lisa Madigan.
Monday's motion does not directly mention Emanuel, who is a candidate in Chicago's Feb. 22 mayoral election.
The latest motion, however, does say the around 100 excerpts help "provide the framework for the importance of the missing December 8, 2008 call" that allegedly involved Emanuel.
Last week, Emanuel downplayed Tuesday's court filing that mentions him, saying he was not concerned about it.
He referred to a "comprehensive review" completed by Obama's White House transition team in 2008 that investigated contacts between Obama aides and Blagojevich aides and found "nothing inappropriate or any deal making."