The United States attorney’s office in Manhattan said in a court filing on Monday evening that it was told that Mr. Giuliani and Mr. Mukasey “have been retained by the defendant and are involved in, and will continue to be involved in, efforts to explore a potential disposition of the criminal charges in this matter.”

Mr. Zarrab, 33, who was born in Iran and moved to Turkey as an infant, has dual citizenship. He was arrested in March 2016 as he arrived on a trip to Miami, and was sent to New York to face charges. Prosecutors, arguing against bail, said Mr. Zarrab had used his considerable wealth and influence to be released from a prison in Turkey after he was detained there in 2013 as part of a corruption investigation of businessmen with close ties to Mr. Erdogan, then Turkey’s prime minister.

Mr. Erdogan has publicly criticized Mr. Zarrab’s prosecution in the United States. According to Turkish news reports, Mr. Erdogan said last fall that he had raised Mr. Zarrab’s case with then-Vice President Joseph R. Biden, Jr. during talks at the United Nations, and Mr. Erdogan also said there were “malicious" intentions in the prosecution, according to the reports.

Mr. Zarrab has been charged with facilitating millions of dollars in illicit transactions on behalf of Iran and other sanctioned entities through the use of front companies and false documentation. Prosecutors have said he “allegedly tricked numerous U.S. financial institutions into processing barred transactions.” Mr. Zarrab has also been charged with conspiracies to commit money laundering and bank fraud. He has pleaded not guilty to the charges, and was ordered detained without bond.

Mr. Zarrab’s decision to retain Mr. Giuliani and Mr. Mukasey was revealed on Monday in a court filing by the office of Joon H. Kim, the acting United States attorney in Manhattan, who took office this month after Preet Bharara was dismissed by the Trump administration.