An adult-film actress who claims she had sex with Donald Trump before he was president says she was threatened in 2011 while with her infant daughter to discourage her from discussing the relationship.

Stormy Daniels, whose real name is Stephanie Clifford, told CBS News’ 60 Minutes on Sunday that she was in a parking lot on her way to a fitness class with her child when an unknown man approached her, according to a transcript of the interview released on Sunday.

“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,” Ms Daniels said.

Ms Daniels sued the President on March 6, alleging Mr Trump never signed an agreement for her to keep quiet about an “intimate” relationship between them.

Ms Daniels’ appearance represented back to back trouble for Mr Trump after an interview broadcast last week on CNN with former Playboy model Karen McDougal, who described a 10-month long affair with Mr Trump starting in 2006.

Mr Trump would have been married to his wife, Melania, during both the alleged extramarital relationships. The First Lady accompanied him this weekend to his Florida golf club.

Stormy Daniels would not say if she had text messages to verify her story. Photo: Twitter

Mr Trump returned to the White House on Sunday but a White House spokeswoman said Melania stayed behind as is her tradition during their son’s school holiday.

Ms Daniels told 60 Minutes she and Mr Trump had sexual relations only once, but that she had seen him on other occasions and he had kept in touch with her.

She said she was not attracted to Mr Trump, who was 60 to Ms Daniels’ 27, in 2006.

The White House has denied he had an affair with Ms Daniels, although Mr Trump lawyer Michael Cohen said he paid her $US130,000 ($168,000) of his own money during the 2016 presidential election campaign.

Mr Trump did not respond to reporters’ shouted questions about whether he would watch the interview when he returned to the White House from Florida.

Mr Cohen, who has denied there was an affair, has not explained why he made the payment or said whether Mr Trump was aware of it.

Recently, Mr Cohen has claimed Ms Daniels is liable for $US1 million every time she breaks the non-disclosure agreement. He alleged she already owed “in excess of” $US20 million and that he “might even taken an extended vacation on her dime”.

Ms Daniels and her lawyers would not discuss in the CBS interview whether they had text messages or other materials that might verify her story.

She was asked why she repeatedly signed statements denying the relationship with Mr Trump, and acknowledged that there could be questions about her credibility.

“I felt intimidated and … honestly bullied. And I didn’t know what to do. And so I signed it,” Ms Daniels said.

Asked why viewers could be confident now that she was telling the truth, she said, “Cause I have no reason to lie. I’m opening myself up for, you know, possible danger, and definitely a whole lot of s–––,” she said.

-with AAP