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Cohen made the assertion in a signed statement filed in federal court Wednesday.
He said in the filing he would assert his Fifth Amendment rights against self-incrimination because of a criminal investigation targeting him, which led to his New York office, home and hotel room being raided by federal agents earlier this month.
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Cohen said federal investigators seized various electronic devices and documents, which he says include information pertaining to a $130,000 payment Cohen made to Daniels to keep her silent about accusations of an affair with Donald Trump.
Trump has denied the affair and knowing anything about the payment.
Daniels, whose legal name is Stephanie Clifford, is suing Cohen and Trump in hopes of being freed from the agreement.
Daniels' lawyer, Michael Avenatti, previously told reporters that he expected Cohen to plead the Fifth Amendment but it was not made official until this filing.
"This is a stunning development," Avenatti said on Twitter Wednesday evening. "Never before in our nation's history has the attorney for the sitting President invoked the 5th Amend in connection with issues surrounding the President."
He added it was an especially "stunning" development since Cohen also served as Trump's "fixer," helping to solve problems before they became bigger issues.
Along with making the payment to Daniels, Cohen also negotiated a $150,000 payment in 2016 from the parent company of the National Enquirer for Karen McDougal, a Playboy model who says she had an affair with Trump.
He's helped pay off others as well, including a former Playboy model who claimed to have been impregnated by a top Republican fundraiser.
Cohen's disclosure comes on the eve of a Thursday court hearing in New York where a federal judge is poised to decide whether to appoint a special master to oversee the examination of documents seized from Cohen's office earlier this month to determine if they should be shielded from federal investigators by attorney-client privilege.
Attorneys for the president asserted in court documents Wednesday that they were capable of such a document review.
"Our own associates … are exceptionally well-qualified, hailing from the country's best law schools and having worked directly with the partners at our firm on complex, confidential government investigations, civil litigation, or both," the Trump lawyers stated in a letter to U.S. District Judge Kimba Wood. "Finally, our client will make himself available, as needed, to aid in our privilege review on his behalf."
Federal prosecutors have argued that no such special master was necessary, saying that a separate division of the Manhattan U.S. attorney's office, known as a filter team, could determine which documents were relevant to the criminal investigation of Cohen and those that were protected by attorney-client privilege.
Contributing: Kevin Johnson. Follow Christal Hayes on Twitter: Journo_Christal