In the filing today, Cohen said the FBI had seized "various electronic devices and documents" that contained information relating to the payment to Daniels, as well as related communications with Cohen's lawyer, Brent Blakely.
"This is a stunning development," Michael Avenatti, a lawyer for Daniels, said in a tweet. "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. It is esp. stunning seeing as MC served as the "fixer" for Mr. Trump for over 10 yrs."
It is not uncommon for defendants facing both civil liability and criminal prosecution to request a pause in civil proceedings to avoid giving sworn testimony and producing documents that could prove incriminating.
Even so, in 2016, Trump sneered at Hillary Clinton aides for exercising their right not to self-incriminate during a congressional investigation into her private email server.
"The mob takes the Fifth," Trump said at one campaign rally, according to AP. "If you're innocent, why are you taking the Fifth Amendment?"
Yet in 1990, Trump himself took the Fifth to avoid answering 97 questions in a divorce deposition, AP noted.
Cohen's lawyers argued last week for a pause in the Daniels case, in the US District Court of the Central District of California. Judge James Otero ordered them to file a declaration from Cohen himself, stating whether he intended to assert his constitutional right against self-incrimination.
Otero must now decide whether there is evidence of enough overlap between the civil case and the criminal investigation to justify a pause.
In New York, lawyers for Cohen and Trump continue to fight for the ability to review material seized in he raids before prosecutors have access to it.
They have argued Cohen should have the ability to decide whether some of the material relates to communications between Cohen and his legal clients and therefore should be shielded from prosecutors' review.
In letters to the court filed today, lawyers for Cohen, Trump and the Trump Organisation said they were prepared to put significant resources into quickly reviewing the documents. A lawyer for Trump wrote that the President himself would be available "as needed" to assist in the process.
Federal District Judge Kimba Wood has ordered that prosecutors let Cohen's lawyers review some of the seized material. She has scheduled a hearing for tomorrow to provide an update on the issue.