Adult film actress Stormy Daniels told CBS' "60 Minutes" she feared for her safety when she signed a strict nondisclosure agreement about her alleged sexual encounter with President Donald Trump's lawyer on the eve of the 2016 presidential election.

Daniels, whose legal name is Stephanie Clifford, said her fear stemmed from an exchange she had in 2011, when she was confronted in a parking lot in Las Vegas by a man who told her not to discuss the 2006 encounter.

"Leave Trump alone. Forget the story," Daniels said the man told her, before turning to focus on Daniels' infant daughter in the back seat. According to Daniels, the man said to her, "That's a beautiful little girl. It'd be a shame if something happened to her mom."

In the CBS interview that aired Sunday, she said that exchange was still on her mind five years later when Trump became the unlikely Republican nominee for president. Through spokespeople, Trump denies that he had an affair with Daniels.

"Suddenly people are reaching out to me again, offering me money. Large amounts of money" to tell about her relationship with Trump, Daniels told "60 Minutes" correspondent Anderson Cooper.

"Was I tempted? Yes – I struggle with it. And then I get the call," she said. Trump's attorney, Michael Cohen, was offering to pay Daniels $130,000 to sign a strict, broad nondisclosure agreement with Trump, she continued.

Read more: Why special counsel Robert Mueller could care about the Stormy Daniels saga

"The story [of the alleged affair] was coming out again. I was concerned for my family and their safety," Daniels told Cooper. "I didn't even negotiate, I just quickly said yes to this very, you know, strict contract — and what most people will agree with me extremely low number."

Daniels' heavily promoted "60 Minutes" interview is unlikely to alter the course of the scandal already brewing over whether the contract with Daniels, signed just 11 days before the presidential election, constituted an illegal campaign donation to the Trump campaign. On CBS, Daniels also reiterated many of the details of an interview she gave In Touch magazine in 2011 but was only published in February.