She was not attracted to Trump and did not want to have sex with him, but: “I didn’t say no. I’m not a victim,” Daniels said, according to an advance transcript of the interview.

She said she stayed in contact with Trump after the encounter because “I thought of it as a business deal,” as the tycoon had said he would try to get her on The Apprentice, the reality TV show he hosted at the time.

At the time, Trump did not ask her not to reveal the encounter, but that changed when she agreed to tell her story to a magazine for US$15,000 in 2011, Daniels said.

“I was in a parking lot, going to a fitness class with my infant daughter … taking, you know, the seats facing backwards in the backseat, diaper bag, you know, gettin’ all the stuff out,” she said.

“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,’” Daniels said.

The experience left her shaking in fear and afraid she would drop her daughter, she added.

Cooper asked: “You took it as a direct threat?”

“Absolutely,” Daniels said.

Daniels said that fear also motivated her to sign the non-disclosure agreement 11 days before the election in 2016.

“The story was coming out again. I was concerned for my family and their safety,” she said.

On her motives for speaking out now, Daniels said she did not see herself as a victim or a part of the “Me Too” movement but simply wanted to set the record straight.

“I’m not okay with being made out to be a liar,” she insisted.

Asked what she would say to Trump if he were watching the interview, she said: “He knows I’m telling the truth.”

The White House has denied any sexual encounter between Trump and Daniels.

Daniels did not, however, discuss evidence to back her encounter with Trump, the possibility of which was teased by her lawyer prior to the interview.

Michael Avenatti posted a picture on Twitter of a computer disc along with the text: “If ‘a picture is worth a thousand words,’ how many words is this worth????? #60minutes #pleasedenyit.”

Avenatti filed a lawsuit on behalf of Daniels – whose real name is Stephanie Clifford – earlier this month seeking to toss out the confidential settlement, under which she was paid by Trump’s personal lawyer, Michael Cohen.

Cohen claimed that Daniels is liable for at least US$20 million for violating the agreement – US$1 million for each time she did so, in a court filing made prior to the CBS interview.

In her interview with Cooper, Daniels described her sexual encounter with Trump beginning with him talking about himself and showing her an issue of a magazine with his picture on the cover. She said she asked, “Does this ... does this normally work for you?” He was taken aback, she says. “And I was like, ‘Someone should take that magazine and spank you with it.’” She says she then ordered him to drop his pants and, in a playful manner, “I just gave him a couple swats.”

She said they talked some more, although he quit talking about himself, and that she became more comfortable.

“He was like, ‘Wow, you — you are special. You remind me of my daughter.’ You know — he was like, ‘You’re smart and beautiful, and a woman to be reckoned with, and I like you. I like you.’”

She said after dinner in Trump’s room, they had sex. He didn’t use a condom, she said, and she didn’t ask him to.

Daniels said Trump called her several times after their initial sexual encounter.

He would ask if they could get together again and that he had an update for her. She said she felt that he was dangling the opportunity to keep her coming back.

“Of course. I mean, I’m not blind. But at the same time, maybe it’ll work out, you know?” Daniels said.

In July 2007, a year after they had met, Daniels said Trump asked to meet with her privately at the Beverly Hills Hotel in Los Angeles. She said they did not have sex, but he wanted to.

Additional reporting by Associated Press