The disclosure came as a NY judge disappointed a lawyer for Trump by letting prosecutors proceed with the cataloguing of evidence including multiple electronic devices that were seized in raids while a system is set up to ensure that records protected by attorney-client privilege aren't disclosed to investigators.
Trump denies that he had sex with Daniels. The hearing followed a raid last week on Cohen's home and office. Prosecutors have defended the search in part by saying that the investigation has shown that Cohen does not do much legal work and does not appear to have many clients. Daniels quietly took a seat towards the back of the public gallery with her lawyer, Michael Avenatti.
Cohen was the target of an Federal Bureau of Investigation raid last week, and the person who paid Daniels $130,000 on the eve of the 2016 presidential election.
The raids were based partly on a referral by the Office of Special Counsel, Robert Mueller who is investigating possible collusion between Trump's 2016 presidential campaign and Russian Federation, according to court filings.More news: Binghamton University cancels classes after second student murder in 5 weeks
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Although communications between lawyers and their clients generally are shielded, the privilege has exemptions, including for criminal activity and fraud.
"The president is very confident in the fact that he has done nothing wrong", White House Press Secretary Sarah Sanders told ABC's "This Week" when asked whether Trump thought Cohen would make a plea agreement.
Last week's raids came after a "months-long" investigation of possible crimes related largely to Cohen's business dealings, rather than his work as a lawyer, prosecutors said in a court filing on Friday.
However, though Avenatti said Daniels's presence at the court had nothing to do with making an impact on Cohen psychologically, he tweeted on Sunday morning a scene from the film "The Godfather II" where a Mafia turncoat retracted his testimony after mafia boss Michael Corleone brought the former's own brother with him to watch the court proceedings.
President Trump's attorneys want a federal judge to throw out all evidence seized in the raid on his personal attorney Michael Cohen's home and office last week.
The president asked that he be able to review before investigators are able to look at anything they took during that time.
Prosecutors say that material should be reviewed by a team of Justice Department lawyers independent from the investigation who could identify records that should remain confidential. Cohen's lawyer is asking for the lawyers themselves to review the material or a "special master" to decide what is relevant to the case, and Hendon is concerned about a taint team or however the material is handled.