Todd Harrison, an attorney for Cohen, urged the judge to issue a temporary restraining order to let either Cohen's lawyers or a court-appointed special master review the materials seized by Federal Bureau of Investigation agents.
While Cohen has admitted to no wrongdoing, the intensity of the government's investigation will put significant pressure on one of the President's closest confidants.
"The government is investigating whether there was, in connection with Trump's White House bid, a conspiracy to commit fraud and extortion for the goal of silencing potentially compromising sources - specifically, people in a position to portray Donald Trump as a womanizer", McCarthy, a senior fellow at the National Review Institute, said.
Earlier on Friday, President Trump had pardoned George W. Bush official Scooter Libby, in what seemed to be a clear signal to his many legally imperiled associates that they need not fear the long arm of the law if they choose to do Trump a solid and not rat on him. Records related to Cohen's taxi medallion business were also sought. Municipal records show Cohen and his wife have 32 taxi medallions in New York City and at least 22 in Chicago.
As McClatchy put it: "Confirmation of the trip would lend credence to a retired British spy's report that Cohen strategized there with a powerful Kremlin figure about Russian meddling in the USA election".
It was quickly adjourned to Monday after another lawyer for Trump interjected that she needed more time to prepare.
Cohen and the company, represented by Brent Blakely, and Trump, represented by Charles Harder, have asked the court to send the case to arbitration - as required by the agreement. The woman's name has not been made public and the source declined to disclose it.
Avanetti then made his argument, to be expended on in another hearing later on Friday.
In an exclusive interview with CNN last month, Davidson described several calls he had with Cohen about striking a deal for Daniels to keep her story quiet. Her allegation was based on a February 13 statement by Cohen that she said hurt her reputation.
Public corruption prosecutors in the U.S. attorney's office in Manhattan are trying to determine, according to one person familiar with the investigation, if there was any fraud related to payments to McDougal or Clifford. Cohen denies having a second passport.
Despite the Cohen matter being unrelated to Mueller's Russian Federation investigation and the obstruction probe into Trump, the FBI raid on Monday infuriated the president and reportedly prompted him and his lawyers to scrap plans for a sit-down interview with Mueller.