Daniels, in papers filed in federal court in NY, claims Trump defamed her when he dismissed as "a con job" a composite sketch of a man she claimed threatened her to stay quiet about their liaison.
"A sketch years later about a nonexistent man".
In accusing Trump of defamation, Daniels said the president knew his April 18 tweet was false or made it with reckless disregard for its truth, and falsely accused her of making up the assailant.
But Ms Daniel's lawyer tweeted that Mr Trump was "well aware of what transpired".
The White House has steadfastly denied the affair. "It'd be a shame if something happened to her mom".
Avenatti, after filing the lawsuit, took his turn on Twitter to accuse Trump of being complicit in the alleged 2011 incident.More news: Amazon Is Turning Vancouver's Old Canada Post Building Into Their New HQ
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Daniels said she did not report the threat at the time because she "didn't want my life to turn upside down".
"Ms. Clifford was shaken by the experience and understood the man's statement to be a direct threat", the suit says.
The sketch depicted a man Ms Daniels described as having threatened her in a Las Vegas parking lot in 2011. He has said the $130,000 payment was legal.
"We look forward to quickly proceeding to discovery and deposing the president", Daniels's attorney Michael Avenatti told Newsweek shortly after the suit was filed, adding he believed it was highly unlikely a judge would dismiss such a "rock solid" case. "I will always protect Mr. Trump", Cohen had said.
Earlier this month, FBI agents raided Cohen's home, hotel room and law offices as part of a criminal fraud investigation.
On Friday, a federal judge in Los Angeles put Daniels' lawsuit against Trump and Cohen on hold for 90 days, due to a pending criminal investigation of Cohen in NY. Sources told ABC News that the Trump campaign payments, which were made between October 2017 and January 2018, were not related to the Daniels case.
Trump is also being sued by a woman named Summer Zervos, who alleged he kissed her forcibly in 2007.