"Mr. Trump's statement is false and defamatory," the lawsuit states.
"In making that statement, Mr. Trump used his national and international audience of millions of people to make a false factual statement to denigrate and attack Ms. Clifford," the suit continues.
In the suit, Daniels is asking for an unspecified amount of monetary damages.
The lawsuit was filed on the heels of a decision by a federal judge in Los Angeles last Friday, which put the Daniel's lawsuit over the $130,000 payment on hold, because of the legal problems being encountered by Cohen, who was the subject of an FBI raid on April 9.
Cohen had told the judge last week that he would exercise his Fifth Amendment rights against self-incrimination; his lawyers, and lawyers for the President are trying to block prosecutors from looking at any documents seized in the raids against Cohen.
In the California lawsuit, lawyers for Mr. Trump had asked for a delay in the proceedings over the case, in which Daniels - whose real name is Stephanie Clifford - wants the court to rule that a non-disclosure agreement involving her and Trump was not valid, because it was never signed by the President.
The judge in that first case granted that delay, but seemed to indicate that he thought Cohen was in serious legal jeopardy.
"Whether or not an indictment is forthcoming, and the court thinks it likely based on these facts alone, these unique circumstances counsel in favor of stay," Judge S. James Otero wrote last week, in agreeing with Mr. Trump's legal team on the need to delay proceedings in that first lawsuit.