Todd Harrison, a lawyer for Cohen, said at Friday's hearing that "thousands" of documents seized were likely privileged, and that many related to clients other than Trump.
Last week's raids came after a "months-long" investigation related largely to Cohen's business dealings, rather than his work as a lawyer, prosecutors have said.
A lawyer for Trump has asked Wood to allow her and the president to decide if any of the documents are protected by attorney-client privilege. The federal prosecutors in Manhattan argued that granting Cohen's lawyers that authority would be unprecedented, and that the use of a special government team would be more appropriate than appointing a special master. Trump will be represented by his own lawyer, Joanna Hendon, who has requested that the president be given a chance to review the seized materials, which includes more than a dozen electronic devices.
Prosecutors have asked that the documents be reviewed for attorney-client privilege by a "filter team" of lawyers within their own office, who would be walled off from the main prosecution team.
Judge Kimba Wood spent more than 2-1/2 hours listening to arguments by Cohen's lawyers, prosecutors from the USA attorney's office in Manhattan and a lawyer representing Trump in the hearing.
United States president's personal attorney Michael Cohen expected to in Federal Court Monday in NY for the resumption of a hearing sought by President after the FBI raided his home and hotel room and he paid $130,000 on the eve of the 2016 presidential election. Stormy Daniels, an adult-film actress, also attended the hearing.
She ordered prosecutors to give Cohen's lawyers a copy of the seized materials before the next hearing. Before disclosing the name, Ryan described him as "a publicly prominent individual" who didn't want to be publicly associated with the Cohen raid.
She turned heads as she entered the courtroom and took a seat in the galley.
But in the background, Cohen also had to contend with Daniels' efforts to keep attention on her story, relating to what she says is a past affair with Trump.
Cohen has admitted that he paid Daniels $130,000 days before the 2016 election.
Daniels, wearing a pink skirt and black heels, stumbled and nearly fell on the wet sidewalk outside the courthouse among a throng of reporters and camera crews.
FILE PHOTO: Fox News Channel anchor Sean Hannity poses for photographs as he sits on the set of his show "Hannity" at the Fox News Channel's studios in New York City, October 28, 2014. Broidy, who has now resigned from the Republican National Committee, paid $1.6 million to a model with whom he had had an affair and who later became pregnant.
Daniels, whose real name is Stephanie Clifford, is suing Cohen for defamation and claimed the nondisclosure agreement she signed is invalid because Trump never signed it. Cohen apparently threatened legal action and the magazine backed down, according to the report.