Daniels' lawyer, Michael Avenatti, filed an amendment to her ongoing lawsuit against Trump, stating Cohen's denial of her claims she had an affair with Trump is a defamatory statement.
"It was reasonably understood Mr. Cohen meant to convey that Ms. [Stephanie] Clifford is a liar," the complaint, which references Daniels' birth name, states. "Mr. Cohen made the statement knowing it was false or had serious doubts about the truth of the statements."
The suit demands the case be tried by a jury and added multiple reasons why the arbitration clause of an agreement she signed before the 2016 presidential election, in which she accepted $130,000 from Cohen to not discuss the affair, is invalid.
In the complaint Avenatti argues the non-disclosure agreement should be ruled "invalid, unenforceable and/or void under the doctrine of unconscionability," stating the $1 million punishment per violation is a random number only "intended to inflict a penalty designed to intimidate and financially cripple" Daniels.
Avenatti alleged Cohen violated the NDA when he disclosed details of the agreement to The Wall Street Journal, making it invalid.
He also said the payment was a violation of campaign finance law stating it was designed to suppress speech "on a matter of public concern about a candidate for Ppresident."
Earlier Monday, deputy White House press secretary Raj Shah said Daniels never had an affair with President Donald Trump and she was never threatened over her allegations.
The White House press corps asked Shah for details about the allegations during the daily press briefing, one day after Daniels described the alleged sexual encounter with Trump several years ago in an interview with 60 Minutes.
Daniels said she met Trump at a celebrity golf tournament in Lake Tahoe in July 2006 when the future president was hosting the NBC reality show, The Apprentice.
Daniels said Trump invited her to his room for sex.
"I realized exactly what I'd gotten myself into. And I was like, 'Ugh, here we go,'" Daniels said with a laugh. "And I just felt like maybe -- it was sort of -- I had it coming for making a bad decision for going to someone's room alone and I just heard the voice in my head, 'well, you put yourself in a bad situation and bad things happen, so you deserve this.'"
Shah denied the affair happened.
"With respect to that interview, I will say the president strongly, clearly and has consistently denied these underlying claims," he said. "The only person who has been inconsistent is the one making the claims."
Daniels, who was 27 at the time while Trump was 60, said that was the only sexual encounter the two had, despite keeping in touch for several months, with Trump occasionally promising to get her a spot on The Apprentice. Eventually, they lost touch.
Daniels said five years after the alleged sexual encounter, in May 2011, she sold her story about having sex with Trump for $15,000 to In Touch.
Anderson Cooper of 60 Minutes said two former employees of the magazine said editors decided not to run the story after they sought comment from Trump and his attorney, Michael Cohen, threatened to sue the publication.
Weeks later, Daniels said a man she hadn't seen before approached her in a gym parking lot while she was with her infant daughter and threatened her if she talked about the encounter.
"A guy walked up on me and said to me, 'Leave Trump alone. Forget the story.' And then he leaned around and looked at my daughter and said, 'That's a beautiful little girl. It'd be a shame if something happened to her mom.' And then he was gone," Daniels said.
Shah said he didn't believe anyone threatened Daniels.
"There is nothing to corroborate her claim," he said.
In October 2016, days before the election, Cohen offered Daniels $130,000 and she took the deal instead of getting more money for telling the story.
"I didn't want to kiss and tell and be labeled all the things that I'm being labeled now," she said. "I didn't want to take away from the legitimate and legal ... career that I've worked very hard to establish. And most importantly, I did not want my family and my child exposed to all the things that she's being exposed to right now. Because everything that I was afraid of coming out has come out anyway, and guess what? I don't have a million dollars."
When asked why the president would pay Daniels to stay quiet about her allegations, Shah said, "false charges are settled out of court all the time."