Presidential spokesman Raj Shah told the briefing, "The president doesn't believe any of the claims Ms Daniels made in the interview last night were accurate."

Asked if Trump believed Daniels was threatened, Shah said, "No, he does not. ... There's nothing to corroborate her claim."

Daniels' "60 Minutes" appearance also drew a denial from the president's personal lawyer, Michael Cohen, that he was involved in the alleged threat of violence against her.

Daniels originally sued Trump on March 6, saying he never signed an agreement for her to stay silent about what she called their "intimate" relationship. Monday's filing in US District Court in Los Angeles amended the original lawsuit to say Daniels was defamed.

Her attorney, Michael Avenatti, said 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" were not true.

Daniels' defamation allegation was based on a February 13 statement by Cohen that she said hurt her reputation.

The latest filing also said $US130,000 Cohen paid Daniels in October 2016 just before the presidential election to secure her silence amounted to an illegal campaign contribution, and that the agreement should be declared void.

Cohen has said he paid Daniels out of his own pocket, but has not explained why or if Trump was aware of the payment.

In filings with the Justice Department and Federal Election Commission, watchdog groups have said the $US130,000 may have exceeded campaign contribution limits, violating US law. Cohen has denied this.

California attorney Michael Overing, who specialises in defamation law, said it would be difficult for Daniels to prevail on her defamation claim because she is a public figure.

To prove libel, she would have to show that a false statement was made with either reckless or purposeful disregard for the truth, Overing said.

Trump attorney Cohen's denial of involvement in the alleged threat against Daniels came in a "cease-and-desist" letter sent to Avenatti shortly after "60 Minutes" aired that demanded a retraction and an apology. A copy of the letter was seen by Reuters on Monday.

The letter said, "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."

Daniels said the threat of harm was made by a stranger in a Las Vegas parking lot in 2011.

Avenatti said on NBC on Monday that the man who threatened her while she was with her infant daughter was not Cohen, but "had to be someone that is related to Mr Trump or Mr. Cohen."

Last week CNN interviewed former Playboy model Karen McDougal, who described a 10-month affair with Trump starting in 2006.

Trump was married to his wife, Melania, during both alleged relationships. In addition to denying Trump had sex with Daniels, the White House has said he denies having an affair with McDougal.