"There's nothing stopping Michael Cohen or his attorneys from coming forward and debating me or offering a contrary position in the press", Avenatti told CNN Friday.
Cohen's legal team in NY is in flux, and his lawyers face a Friday deadline to finish reviewing documents seized in Federal Bureau of Investigation raids on his home and office.
Michael Avenatti, who represents Daniels in separate civil litigation against Cohen and Trump, on Friday tweeted that the encrypted messages and reconstructed documents "could pose a huge problem for Mr. Cohen and ultimately Mr. Trump".
A federal judge agreed in April to delay the case for 90 days after Cohen argued that the criminal investigation overlapped with issues in the lawsuit and his right against self-incrimination would be adversely affected because he won't be able to respond and defend himself.
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Clearly Avenatti is getting under Michael Cohen's skin. Trump subsequently acknowledged that he reimbursed Cohen for that payment. Under the supervision of a retired federal judge acting as a "special master", the files are being scrutinized by Cohen's attorneys for items potentially covered by attorney-client privilege.
He wants a judge to sign a restraining order that would prohibit Avenatti from speaking with reporters or publicly releasing details about the case. Jones reviews the designations, then makes recommendations to Wood, who has the final say.
In a brief order, U.S. District Judge James Otero in Los Angeles said Cohen had not shown he would face "immediate, irreparable injury" without an immediate restraining order.
The criminal probe into Cohen's business dealings stems in part from a referral by Special Counsel Robert Mueller, who is investigating whether Trump's 2016 campaign colluded with Russian Federation to influence the US presidential election.
Daniels, whose real name is Stephanie Clifford, is suing Cohen and Trump to get out of an agreement under which Cohen paid her $130,000 not to discuss an alleged sexual encounter she had with Trump. But an additional 315 megabytes of data have been pulled from the first of the two BlackBerries, and its contents were delivered to Cohen's attorneys on June 14.