Donald Trump won’t tweet about Stormy Daniels because alleged affair is true, her lawyer says

U.S. President Donald Trump has restrained himself from tweeting about adult film star Stormy Daniels and her claims of a sexual encounter with him because the allegations against the president are true, according to her lawyer.

Michael Avenatti, the attorney representing Daniels, whose legal name Stephanie Clifford, told CBS This Morning he believes that Trump has been mute on social media about his client because her claims against him are true.

“Isn’t it interesting, Gayle, that we have a president that will tweet about the most mundane matters but he won’t tweet about my client, the (alleged) affair, the agreement, or the $130,000 payment,” Avenatti mused while speaking to co-host Gayle King. “You know why he won’t tweet about it? Because it’s true. It’s 100 per cent true.”

READ MORE: Stormy Daniels says she was threatened to remain silent over alleged Trump affair

Avenatti’s comments come a day after his client told her story in a sit-down interview with 60 Minutes that aired Sunday evening. During the interview, Clifford said she had been threatened in 2011 to discourage her from discussing her apparent relationship with Trump. At the time of the threat, she says, she was in a parking lot with her infant daughter.

WATCH: Stormy Daniels’ lawyer says large majority of Americans believe her ‘credible’ after interview

“And 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,” Clifford said.

On Monday, Avenatti said he was still “in the process to discover” who made the threat against his client.

“She receives threats on a near hourly basis,” the lawyer told CBS. “Now, we don’t have anything tying those to Mr. Cohen [Trump’s lawyer, Michael Cohen] or Mr. Trump to be clear, but she’s certainly scared for her safety and the safety of her family in light of this.”

WATCH: Stormy Daniels’ lawyer says ‘cover up’ of alleged affair with Trump should matter to public

Daniels received a $130,000 payment days before the 2016 presidential election for her silence and has sought to invalidate a non-disclosure agreement.

Trump, through his representatives, has denied the allegations. His attorney, Michael Cohen, has said Trump never had an affair with Daniels. Cohen has said he paid the $130,000 out of his pocket.

READ MORE: Stormy Daniels’ lawyer says he has DVD containing proof of porn star’s affair with Trump

On Monday, Cohen’s attorney, Brent H. Blakely, denied that Cohen had anything to do with the threat.

WATCH: On “60 Minutes”, adult film star Stormy Daniels tells Anderson Cooper she was in a parking lot on her way to a fitness class when a man walked up to her and said, “Leave Trump alone. Forget the story.”

“In truth, Mr. Cohen had absolutely nothing whatsoever to do with any such person or incident, and does not even believe that any such person exists, or that such incident ever occurred,” he said, demanding that Daniels “cease and desist from making any further false and defamatory statements about my client.”

Also on Monday, Trump tweeted about “fake news,” but it’s unclear what he may have been referring to.

“So much Fake News. Never been more voluminous or more inaccurate. But through it all, our country is doing great!” the president tweeted.

–with files from the Associated Press