The prosecutors also noted that "in addition to his comments on the evidence and witnesses, Shkreli also made inappropriate personal attacks on current and former prosecutors in this case."
According to the Associated Press, Shkreli lawyer Brafman objects to the prosecutors' request, and said "certain representatives of the press have gone out of their way to try to 'bait'" Shkreli into commenting.
The AP also quoted Brafman as saying Shkreli is "under enormous pressure that is compounded by his clearly frail emotional state."
The prosecution's unusual request, made on the eve of the Fourth of July, came after Shkreli, stunned reporters, his lawyers and others by effectively holding a press conference in a courtroom down the hall from the one where his trial was being held.
Shkreli criticized the United States Attorney's Office for the Eastern District, which is prosecuting him, as the "junior varsity," claimed he never considered taking a plea deal and said people "blame me for everything."
Shkreli also griped about news headlines regarding his case, and teed off on a young woman who had testified that he had dragged out redeeming her $435,000 investment in his hedge fund for almost a year, saying she wasn't a "victim."
He claimed her investment quadrupled.
And Shrkreli said that several documents entered into evidence, which have raised questions about his honesty with investors, were prepared by others.
"Do I want to exonerate myself?" he asked. "Yes."
"They blame me for everything," Shkreli said, apparently referring to prosecutors and his other critics.
"Blame me for capitalism," Shkreli said. "Blame me for EpiPen."
Several prospective jurors earlier this week were excused from consideration because they incorrectly believed Shkreli had raised the price of the anti-allergy device EpiPen.
In reality, Shkreli drew widespread public scorn in 2015 for hiking the price of an anti-parasite drug named Daraprim by more than 5,000 percent while serving as CEO of Turing Pharmaceuticals.
Last Friday, Shkreli only stopped talking and left when his high-powered lawyer Brafman peered in the room and asked, "Martin, can I talk to you for a minute?"
Brafman later said he would prefer Shkreli not conduct any more impromptu press conferences "because sometimes he doesn't have a filter."
"I'm hoping he doesn't do it ever again," Brafman told reporters.
Shkreli is charged with securities fraud in connection with his alleged looting millions of dollars from Retrophin, the publicly traded drug company he founded. Prosecutors claim he used the money to repay investors whom he allegedly defrauded at two hedge funds he had run, in addition to paying off personal debts.