Daniels said in a "60 Minutes" interview that aired Sunday that she was threatened by an unidentified man in Las Vegas to keep quiet about her alleged relationship with Trump. "It'd be a shame if something happened to her mom.'" Daniels said she did not report the incident to police because she was scared.
At Monday's press briefing, White House spokesman Raj Shah said that Trump doesn't believe that any of the claims "that Ms. Daniels made last night in the interview are accurate".
Shah, asked whether Trump believed Daniels, whose real name is Stephanie Clifford, was threatened, said, "No, he does not".
Daniels, 39, said that she was threatened in 2011 over the affair after agreeing to speak to a US celebrity gossip magazine.
Daniels' appearance represents back-to-back trouble for Trump after an interview broadcast last week on CNN with former Playboy model Karen McDougal, who described a 10-month-long affair with Trump starting in 2006, apparently at the same golf tournament Daniels says she first met the future president.
Daniels amended her existing lawsuit against Trump, adding Cohen as a defendant in the pending case.More news: Palestinian Ahed El-Tamimi Jailed for 8 Months in a Plea Deal
Watchdogs have alleged the $130,000 payment may have constituted an undeclared campaign contribution, but the White House on Monday denied doing anything illegal.
"Mr. Cohen paid the 130,000 dollars, but the reason is to protect business, protect reputation, and to protect family, and you can not speculate that it was to elect somebody President of the United States", said Cohens' attorney, David Schwartz.
Daniels attorney Avenatti said on NBC on Monday morning that the man who threatened his client while she was with her infant daughter was not Cohen but that "it had to be someone that is related to Mr. Trump or Mr Cohen". "The only person who has been inconsistent is the one making the claims", Shah said in a statement. "You remind me of my daughter [Ivanka]". Trump returned to Washington from Palm Beach on Sunday, while Melania Trump remained in Florida on a pre-scheduled spring break with the couple's 12-year-old son, Barron.
The interview gave "60 Minutes" its biggest audience in a decade, with slightly more than 22 million viewers tuning in, according to Nielsen Co. estimates.
She claimed in 2011, when she was trying to sell her story about her relationship with Mr Trump, she got what she thought was a direct threat. Mr Trump allegedly to her: "Don't worry about that". It also alleges that Cohen was secretly involved in her discussions with American Media.