Trump has acknowledged paying Daniels, via Cohen, $130,000 in exchange for her keeping silent about the sexual encounter she alleges she had with Trump in 2006.
At a hearing on Tuesday, Trump's lawyer, Marc Kasowitz, argued unsuccessfully before Manhattan Supreme Court Justice Jennifer Schecter that Zervos' lawsuit should not go forward until the New York Court of Appeals, and if necessary, the U.S. Supreme Court, decides the issue.
Zervos has alleged that Trump groped her when she sought career advice from him in 2007.
"It's definitely the case to the extent that plaintiff seeks discovery from other women who are not parties to this case, who are not making a claim of defamation, we would take a position that that evidence would not be covered", Kasowitz said.
A judge in NY state trial court has ordered that depositions in a lawsuit against President Trump must be complete by early next year, setting up a potential showdown over whether Trump must answer questions under oath. Trump has argued that as a sitting president he is immune from the lawsuit and is seeking an order from New York's highest court freezing the case.
Top US Senate staffer charged in leak investigation
They added that "the charges do not appear to include anything related to the mishandling of classified information". Wolfe was arrested and indicted on charges of lying to the FBI on Thursday as part of that investigation.
Presidential depositions have a memorable history: During a 1998 deposition in a sexual harassment case filed by Paula Jones, then-President Bill Clinton denied a sexual relationship with White House intern Monica Lewinsky.
The Republican denied all of the claims, saying they were "100 percent fabricated" and "totally false" and his accusers were "liars". They also argue that a sitting president can not be sued in a state court.
There is also the matter of the several other women who have accused Trump of various degrees of sexual misconduct. "He specifically contested Zervos" allegations in a statement and retweeted a message that included her photo and described her claims as a "hoax, ' " The Associated Press reports.
Ms Zervos said his words hurt her reputation, harmed her business and led to threats against her. Trump is now asking the Court of Appeals to impose a stay. Griffin, who lost her New Year's Eve hosting duties at CNN and has been ostracized by many in Hollywood, apologized, but later retracted it.
Trump's lawyers are seeking a court order to keep documents and information private; the details are yet to be worked out.
Trump's attorneys have said his statements were true, and also that his remarks were "non-defamatory opinions" that came amid the heated public debate of a national political campaign.
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