The White House hit back at porn star Stormy Daniels on Monday, insisting there was "nothing to corroborate" her claims of extramarital sex with Donald Trump.

In its first response to a primetime interview watched by more than 21 million Americans, the White House questioned Daniels' credibility and challenged her to present proof.

"The president has strongly, clearly and has consistently denied" allegations of sexual liaison, White House spokesman Raj Shah said.

Trump has never spoken publicly about the allegations and has repeatedly ignored questions from reporters about the issue, which has dogged the White House for months.

On Monday morning, Trump tweeted cryptically: "So much Fake News. Never been more voluminous or more inaccurate. But through it all, our country is doing great!"

The CBS interview on Sunday night brought the 39-year-old's long-simmering allegations of sex, hush money and intimidation to a national audience directly for the first time.

Daniels alleged the pair had unprotected sex after meeting at a celebrity golf tournament in Lake Tahoe in July 2006 — shortly after Trump's wife Melania gave birth to their son.

'Near-hourly' threats

Daniels told Anderson Cooper on CBS's "60 Minutes" that five years later she was approached by a man in a Las Vegas parking lot and warned to keep silent, after she had agreed to sell her story for $15,000.

Her lawyer, Michael Avenatti, told MSNBC on Monday that his client is receiving "threats on a near-hourly basis" and that "she's certainly scared for her safety and the safety of her family."

Trump's lawyer Michael Cohen has admitted paying Daniels $130,000 shortly before the 2016 election, but has not explained why.

"The president doesn't believe any of the claims Ms Daniels made in the interview last night were accurate," Shah said, while admitting Trump may not have watched it all.

"There's nothing to collaborate her claim," Shah added, going a step further and accusing her of changing her story.

"The only person who's been inconsistent is the one making the claims," he said, citing documents she signed denying the affair.

Daniels, whose real name is Stephanie Clifford, has acknowledged she signed a non-disclosure agreement, with a potentially ruinous fine of $1 million every time she speaks about the alleged tryst.

She is challenging the validity of the agreement in court.

Such contracts, while legal, have frequently been used by powerful men to hush up affairs, workplace harassment or even alleged sexual abuse.

Evangelical support

Avenatti said on Monday that the suit has now been expanded to accuse Cohen of defamation.

"We have added an allegation or claim of defamation against Mr Cohen for his previous denials of the affair — basically calling my client a liar," he told MSNBC.

Daniels is seeking both punitive damages and legal costs from Cohen, according to a court document filed on Monday.

The issue is a difficult one for Trump, potentially undermining his support among evangelical voters, fueling legal jeopardy and causing friction with the East Wing of the White House, where First Lady Melania Trump has her offices.

So far, she has not responded, but her spokeswoman Stephanie Grisham urged respect.

"While I know the media is enjoying speculation & salacious gossip, I'd like to remind people there's a minor child who's name should be kept out of news stories when at all possible," she tweeted on Sunday.

Watchdogs have alleged the $130,000 payment may have constituted an undeclared campaign contribution, but the White House on Monday denied doing anything illegal.

"I can speak for only the White House. And I can say categorically that, obviously, the White House didn't engage in any — any wrongdoing," said Shah.