They argued in a new court filing Tuesday that prosecutors demonstrated "appalling disregard" for Adams' rights.
The mayor's lawyers accused prosecutors of leaking grand jury material and other sensitive information in "brazen violations" of the rules.
Defense attorney Alex Spiro asked for an evidentiary hearing and sanctions.
Adams is due in court Wednesday for an initial hearing with the trial judge. He has already sought to dismiss the bribery charge, arguing his alleged conduct does not meet the legal definition of bribery.
Adams has pleaded not guilty to a five count indictment accusing him of engaging in a years long conspiracy to take illegal foreign money.
It comes the morning after one of Adams' closest aides resigned late Monday, just days after the New York City Mayor was indicted on corruption charges.
Timothy Pearson is the fifth senior member of the administration to announce his departure in the past three weeks.
Pearson, a former high-ranking official in the police department, served as a senior advisor on public safety to the mayor. He's been named in multiple lawsuits as he's currently under investigation by another city agency for his role in a brawl at a shelter for homeless migrants.
The FBI had seized his phone a month ago and served him a subpoena.
Pearson "wanted to focus on another aspect of his life and deal with those items that he has he has to deal...he's moving on to the next level," Adams said.
Pearson adds to a list of resignations from Adams camp, including former police commissioner Edward Caban, schools chancellor David Banks, chief legal advisor Lisa Zornberg, and health commissioner Ashwin Vasan.
On Tuesday, the mayor announced he is filling his top two legal positions. He is nominating the city's acting corporation council, Muriel Goode-Trufant, to permanently fill the role. She will have to be confirmed by the City Council, which rejected his last choice, Randy Mastro.
He is also filling the role of Chief Council with Allison Stoddart for the position vacated by Zornberg.
ABC News' Aaron Katersky contributed to this report.
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