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President Donald Trump's lawyer is trying to silence adult-film star Stormy Daniels, obtaining a secret restraining order in a private arbitration proceeding and warning that she will face penalties if she publicly discusses a relationship with the president, NBC News has learned.

The new pressure on Daniels, whose real name is Stephanie Clifford, comes a day after she filed a lawsuit in a Los Angeles court alleging that a nondisclosure agreement she made to keep quiet about an "intimate" relationship with Trump is invalid because he never signed it.

Tuesday's lawsuit says that Trump attorney Michael Cohen — who brokered the agreement with Clifford during the presidential campaign — attempted to "intimidate" Clifford and "shut her up" by initiating what it calls a "bogus arbitration proceeding" against her in Los Angeles on Feb. 27.

On that day, Cohen obtained a temporary restraining order against Clifford from the private arbitrator, a retired judge, which bars her from disclosing "confidential information" related to the nondisclosure agreement signed in October 2016, according to a copy of the order obtained by NBC News.

Read the temporary restraining order against Stormy Daniels

On Feb. 28, Cohen emailed the restraining order to Clifford's former attorney, Keith Davidson. "The document itself is to remain confidential and not to be disclosed to anyone as per the terms of the judge's order," the email, obtained by NBC News, said.

Reached for comment late Wednesday afternoon, Clifford's current attorney, Michael Avenatti, said Cohen, through his own attorney, Lawrence Rosen, has made further attempts to enforce the order and caution Clifford that she is subject to damages if she talks about Trump.

"Earlier today, Mr. Cohen through his attorney, Mr. Rosen, further threatened my client in an effort to prevent her from telling the truth about what really happened," Avenatti said. "We do not take kindly to these threats, nor we will be intimidated."

Cohen and Rosen did not immediately respond to requests for comment from NBC News.

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But Rosen, who has represented Trump and his companies in the past, said in a statement to other media outlets that the agreement with Clifford contained an arbitration clause with permission to "seek an injunction in the event of a breach or threatened breach of the agreement."

“The designated judge from the arbitration tribunal found that Ms. Clifford had violated the agreement and enjoined her from, among other things, filing this lawsuit," Rosen said in the statement.

White House spokeswoman Sarah Huckabee Sanders said in a press briefing Wednesday that Trump denies "all of these allegations" — that he had an affair with Clifford more than a decade ago or that he knew Cohen had paid her $130,000.

"I have had conversations with the president about this and as I outlined earlier, this case had already been won in arbitration," Sanders said. It's unclear what Sanders was referring to; Trump is not listed as a party on the restraining order issued by the arbitration judge.

Asked about that comment, Avenatti quipped, "Yeah, and he won the popular vote, too."

Analysis: Stormy Daniels isn't suing Donald Trump for cash

“President Trump hasn’t won anything relating to Ms. Clifford," he added.

"First of all, it does not appear as if he was even a party to the arbitration Ms. Sanders is referring to. How can you win something you’re not even a part of? Secondly, claiming that Mr. Trump ‘won’ at arbitration when there has been no hearing, no notice to Ms. Clifford, no opportunity given to her to respond, and no decision on the merits, is completely bogus."

Earlier on Wednesday, Avenatti told "Today" that Clifford's lawsuit, if successful, would allow his client to "tell her story."

"She believes it's important that the public learn the truth about what happened," he said. "I think it's time for her to tell her story and for the public to decide who is telling the truth."

The suit asks a California court to affirm that the agreement Clifford signed is invalid.

The "hush agreement," as it's called in the suit, refers to Clifford as Peggy Peterson and another individual as David Dennison. In one of the documents, the true identity of Dennison is blacked out, but Avenatti said the individual is Trump.

Clifford signed both the agreement and a side letter agreement using her professional name on Oct. 28, 2016, just days before the 2016 presidential election. Cohen signed the document the same day. Both agreements were appended to the lawsuit as Exhibit 1 and Exhibit 2.

Each document includes a blank where "DD" is supposed to sign, but neither blank is signed.

Clifford and Trump had an intimate relationship that lasted from the summer of 2006 "well into the year 2007," and meetings in Lake Tahoe and at the Beverly Hills Hotel, the lawsuit alleges. In the past, Cohen has said the president denies there was ever a relationship.

The lawsuit says that Cohen — who says he used his personal funds to facilitate a payment to Clifford — has been trying to scare the actress into not talking.

"To be clear, the attempts to intimidate Ms. Clifford into silence and 'shut her up' in order to 'protect Mr. Trump' continue unabated," says the suit. "On or about February 27, 2018, Mr. Trump's attorney Mr. Cohen surreptitiously initiated a bogus arbitration proceeding against Ms. Clifford in Los Angeles."

The nondisclosure agreement said any further dispute would be resolved by binding arbitration "to the greatest extent permitted by law."

If the agreement is void because Trump didn't sign it, as Clifford argues, the arbitration clause would also be unenforceable.