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Daniels added Trump’s attorney, Michael Cohen, to a lawsuit filed against Trump, saying he had defamed her by claiming she lied about her relationship with the president

The White House has attacked the credibility of Stormy Daniels, the adult film star who spoke out on US TV on Sunday night about her alleged affair with the president and threats she said she received. Concurrently, the legal battle between Daniels and Trump’s personal attorney, Michael Cohen, grew fiercer.

Stormy Daniels interviewed by Anderson Cooper – the key moments Read more

Speaking from the podium of the White House press briefing room on Monday afternoon, administration spokesman Raj Shah said: “With respect to that interview, I will say the president strongly, clearly has consistently denied these underlying claims. The only person who’s been inconsistent is the one making the claims.”

Shah did not mention Daniels by name. Trump “denied the claims she made last night” he said. “He has been consistent in doing so, she has not”.

Shah spoke hours after Cohen’s own lawyer, Brent Blakely, wrote to Daniels’ attorney to say she had made false and defamatory comments, “namely that [Cohen] was responsible for an alleged thug who supposedly visited” and threatened her.

“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,” Blakely said in the letter, according to Reuters.

In response, Daniels – whose real name is Stephanie Clifford – added Cohen to a lawsuit previously filed against Trump, saying he had defamed her by claiming she lied about her relationship with the president. In a court document, Daniels said “it was reasonably understood Mr Cohen meant to convey that Ms Clifford is a liar, someone who should not be trusted, and that her claims about her relationship with Mr Trump is ‘something [that] isn’t true’.”

Facebook Twitter Pinterest Michael Cohen says he does not believe the alleged threat against Stormy Daniels ever occurred. Photograph: Richard Drew/AP

In the CBS 60 Minutes interview broadcast on Sunday, Daniels said she was threatened with physical violence after she first attempted to go public with the story. She was on her way to a fitness class with her infant daughter in Las Vegas in 2011, she said, when she was accosted in a parking lot.

“A guy walked up on me,” she said, “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 she did not know who the man was and did not link him to Cohen. Later, however, when explaining why she signed a document in 2016 that denied any affair with Trump, she said she was told that if she did not, “they can make your life hell in many different ways”.

Asked who “they” were, Daniels said: “I’m not exactly sure who they were. I believe it to be Michael Cohen.”

The interview attracted 22 million viewers, 60 Minutes’ highest ratings in a decade. Shah declined to say if Trump watched. “I’m not going to get into what the president may or may not have seen,” he told reporters.

Early on Monday morning, Stephanie Grisham, a spokeswoman for Melania Trump, the president’s wife, slammed the media for enjoying “speculation & salacious gossip” and added: “I’d like to remind people there’s a minor child who’s [sic] name should be kept out of news stories when at all possible.”

Melania was not with Trump when the show aired. The White House announced that she would spend the week in Florida with their son, “as is their tradition for spring break”. Trump stayed silent, other than a tweet about “so much Fake News”.

“Never been more voluminous or more inaccurate,” the president wrote. “But through it all, our country is doing great!”

Representatives for the president have denied any sexual relationship with Daniels, despite Cohen’s admission that he paid $130,000 to buy her silence. Cohen claims to have paid that sum out of his own pocket.

Daniels’ lawyer, Michael Avenatti, called that “ludicrous” during the CBS broadcast. On Monday, Avenatti said he would not yet reveal what he implied was additional evidence to back up Daniels’ claims.

“We’re not going to get into the details of everything we have at this time, and there’s a reason for that,” he said on NBC’s Today show. “We understand the American people want all the information right now, immediately. It would make no sense for us to play our hand as to this issue and we’re not going to do it right now.”

He also said the unidentified man Daniels said threatened her in 2011 must have been linked to Trump.

The allegation that someone threatened Daniels takes the dispute between the president and the porn star to a new level. Until now the issue has been her claim of a sexual relationship – although Daniels told CBS they had sex only once, in 2006 – and Trump’s denials, as well as a legalistic argument over whether the non-disclosure agreement signed by Daniels 11 days before the 2016 election is binding.

Q&A Who are the 20 women accusing Donald Trump of assault and harassment? Show Hide Jessica Leeds Ivana Trump Jill Harth Kristen Anderson Lisa Boyne Cathy Heller Temple Taggart Mariah Billado Karena Virginia Bridget Sullivan Tasha Dixon Melinda McGillivray Jennifer Murphy Rachel Crooks Natasha Stoynoff Ninni Laaksonen Jessica Drake Samantha Holvey Summer Zervos Cassandra Searles Read the full details of the 20 accusations here

Daniels’ claim of an affair in 2006 bears striking similarities to an account given last week by a former Playboy model. Karen McDougal told CNN she had an intense relationship with Trump in 2006 and 2007, and that he once took her to his Manhattan home. Both McDougal and Daniels allege that their encounters occurred within months of the birth of Barron, Trump’s son with Melania.

A large number of women have accused Trump of sexual assault. He denies the claims.