They also accused Avenatti, with his non-stop series of appearances on television about the case, of "smearing" Cohen in order "to further his own interest" in gaining media attention.
"To our knowledge, this Court has never been presented with clearer evidence of the deliberate creation of a carnival atmosphere and inappropriate conduct while an attorney's application for admission was pending," Cohen's lawyers wrote.
Avenatti, who is not admitted to federal court in New York, is asking Judge Kimba Wood to be admitted pro hac vice — meaning solely for the purposes of Cohen's case — to speak on Daniels' behalf.
Files related to Daniels, and to a $130,000 hush money payment she received in October 2016 from Cohen, were reportedly among documents seized from Cohen by the FBI during raids on his home, office and hotel room on April 9.
Daniels has said the money was in exchange for her silence about an affair with Trump, an affair that the White House has denied. Avenatti is representing Daniels in a lawsuit against Trump and Cohen to void the contract she signed.
While prosecutors are investigating Cohen for business dealings, as well as the payment to Daniels, they have not charged him.
Since the raids, however, there have been several court hearings and multiple legal filings related to how to handle the documents and electronic files seized from Cohen.
Trump's own lawyers, as well as lawyers for the Trump Organization, have been admitted to the case so that they can argue about documents that might be subject to protection from prosecutors' eyes because of attorney-client privilege.
Cohen's lawyers noted that Daniels has another lawyer who is admitted to New York federal court, who can speak for her if Avenatti's request for admission is denied.