Avenatti spoke outside the court at Friday's hearing and then followed with a suggestive tweet that "the weather forecast for Monday looks very Stormy".
Trump attorney Joanna Hendon also asked that prosecutors be temporarily prohibited from reviewing the paperwork.
"The (US Attorney) and Federal Bureau of Investigation have reason to believe that Cohen has exceedingly few clients and a low volume of potentially privileged communications", the Justice Department motion said.
In an interview, Avenatti said he wants to make sure "that the integrity of the documents, whatever was seized, is maintained".
Investigators have also been looking into a blueprint of tax evasion, fraud, money laundering as well as other possible offenses in Cohen's agreements, for example his work to Trump plus several true estate trades the origin mentioned.
The filing, signed by acting U.S. Attorney Robert Khuzami in the Southern District of NY, also says that while the current investigation was referred by special counsel Robert S. Mueller III, the NY investigation "has proceeded independent" of Mueller's work.
The afternoon portion of the hearing came after a hectic morning before Wood.
In a court filing on Friday, federal prosecutors confirmed that Cohen was over his firm transactions rather than his private work, chiefly under legal investigation for decades.More news: Unnao case: BJP MLA's wife meets DGP, demands independent probe
Cohen was photographed outside the Loews Regency Hotel on Park Avenue in New York City on Friday.
Federal prosecutors revealed on Friday that Cohen has been the subject of a criminal investigation for months.
Michael Cohen, left, President Donald Trump's personal attorney, stands with his attorney Stephen Ryan on September 19, 2017, after finding out the Senate Intelligence Committee hearing at which they were to appear was canceled.
Outlets say a hearing to address Cohen's restraining order request is scheduled for Friday.
Though the status of the relationship between the porn star and the president remains tentative, Trump and Cohen's lawyers went to court in an effort to stop the Justice Department from reading seized documents.
Agents with the Federal Bureau of Investigation raided Cohen's NY office and home this week, partly based on a referral from Mueller.
President Donald Trump's personal attorney is trying to prevent the government from using materials it found in a search of his office and residence this week.
They involve burying stories about Trump in connection with adult actress Stormy Daniels and Playboy model Karen McDougal, said McCarthy, and on reports that a former Trump building doorman was paid $30,000 to stay quiet about an unverified claim that Trump, 30 years ago, allegedly fathered a child with a Trump Organization employee.