The judge said she needed to balance the need for a careful review with the need to move the case forward and noted that the special master, who is also reviewing documents as they are produced by the government, had no problem "speeding up as necessary".
Ryan's first point of concern remains Avenatti's role in the release of information about a bank account used by Cohen to allegedly pay Clifford $130,000 in hush-money ahead of the 2016 presidential election.
Wood also heard from Cohen's legal team about the progress it was making on reviewing materials seized from Cohen's office, residence and hotel room in an Federal Bureau of Investigation raid last month.
U.S. District Judge Kimba Wood said a special taint team of prosecutors will make determinations after that date.
That process is being overseen by former judge Barbara Jones, whom Wood appointed "special master" in the matter.
"I don't know if we can make that", another Cohen lawyer, Stephen Ryan, said of the June 15 deadline.
She said lawyers for Cohen, Trump and the Trump Organization had made 252 total privilege designations from materials produced by the government on May 8 and May 9.
Wood gave Cohen's team until June 15 to review the seized documents and electronic files or she'll allow Justice Department lawyers to finish the job.
Stormy Daniels' lawyer Michael Avenatti must stop his "publicity tour" if he wants to be a part of a court proceeding about materials seized in a criminal probe of President Trump's personal lawyer Michael Cohen, a Manhattan federal judge said Wednesday. He said this was "very surprising and disturbing to me" as an attorney for Daniels, whose real name is Stephanie Clifford.More news: North Korea to build 2,000 homes near airport, state media say
Trump has denied all wrongdoing, as has Cohen.
"Lawerence, this is pathetic", Avenatti said.
The attorney for porn actress Stormy Daniels appeared Wednesday evening on MSNBC's "The Beat With Ari Melber", where the host asked him to speculate about what those tapes might reveal about the president and his Trump Organization attorney. Cohen's attorneys and Avenatti have engaged in an extended back-and-forth over the question, filing dueling letters Tuesday night and then arguing in court Wednesday. "It's really not a good idea if are you going to do that, to record them with people that later become the president of the United States".
Upon leaving the courthouse in lower Manhattan, Cohen - who also has the Fox TV star Sean Hannity as a client - did not reply to a shouted question about whether he meant to cooperate with prosecutors.
After the hearing, Avenatti withdrew his motion to intervene - at least until the court rules whether Daniels is allowed to participate in the case. This material, she said, would be turned over to Cohen's team as soon as possible.
Jones wrote in a filing submitted Tuesday night that after her reviews so far, the U.S. Attorney's Office for the Southern District of NY has been given access to more than 292,000 items, and more than 1 million items "not designated privileged or highly personal" were expected to be released Wednesday. In a report earlier this month, Jones said the government turned over electronic data from the contents of telephones and iPads on those days.
The raids on Cohen were triggered in part by a referral from special counsel Robert Mueller, who separately is looking into Russian interference in the 2016 USA presidential election.
Cohen and his attorney's "are hell bent on continuing to hide the truth from the American people", Avenatti told reporters after court.