His lawyers asked a US judge Friday to let them review the information before FBI investigators go through it so they can highlight what's covered by privilege. Wood ordered Cohen to be present at the hearing.
A White House spokesman referred a request for comment to Mr Cohen and his attorney. Avenatti said he thinks that some of the documents obtained from the Cohen search relate to his client.
Such an order would be sought to stop the government from using seized materials, according to a person familiar with the investigation.
The U.S. Attorney's office in Manhattan turned in the filling after a judge denied an attempt by Cohen and Trump to stop investigators from reviewing material the Federal Bureau of Investigation seized in a search of Cohen's office and residence Monday. The raid can be traced back to special counsel Robert Mueller's investigation into Russian election meddling and any ties to the Trump campaign.
But the prosecutors say they have already conducted searches of Cohen's email accounts, which they say "indicate that Cohen is in fact performing little to no legal work, and that zero emails were exchanged with President Trump".
Trump lawyer Joanna Herndon, who said she was hired on Wednesday, asked for the adjournment to give the president's legal team time to make arguments.
At the outset, Harrison brought up his concerns about how the government meant to proceed with the material the government seized during the raids. In a footnote in its filing, the prosecutors expressed doubt that any communications between Trump and Cohen regarding a payoff to Daniels before the election would be covered under attorney-client privilege. Hendon asked for a delay in court proceedings until at least Monday, saying she needed to research the law.
McKay argued that a so-called "Filter Team" from the justice department should be allowed to check all the seized documents for possible privilege. It sounds like he knows there is more to come regarding the SDNY's Michael Cohen investigation, and now it's becoming clear why. She also raised concerns about "innocent parties" having their privacy violated based on material being discussed.
The judge also heard a request from Michael Avenatti, Daniels' lawyer, to weigh in on the files because they likely involved her, and the judge consented.
"I would have to check", she told reporters at the daily briefing.
Sources told CNN agents were looking for communications that Trump may have had with Michael Cohen, the lawyer, related to the infamous tape in which the president said he could "grab" women by their privates and will sometimes "just start kissing them ... just kiss, I don't even wait".
"He continued to struggle to hire a new criminal lawyer", the Times noted, "and some of his own aides were reluctant to advise him about a response for fear of being dragged into a criminal investigation themselves".
The raids infuriated Trump, who tweeted "Attorney-client privilege is dead!" on Tuesday. Or, they said, the court could appoint a special master for that objective.
The court is scheduled to take the issue back up at 2 p.m. Monday.
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