Adult film actress Stormy Daniels says she was threatened to keep quiet about an alleged sexual encounter with Donald Trump in 2006.
The actress - whose real name is Stephanie Clifford - told CBS News a man had approached her in a Las Vegas car park in 2011.
The stranger allegedly said "leave Trump alone", then looked at her young daughter and added: "It'd be a shame if something happened to her mom."
Mr Trump strongly denies having had an affair with the actress.
His lawyers are seeking $US20m in damages from her, saying she broke a non-disclosure deal signed before the 2016 presidential election. She says the claim is invalid.
Ms Clifford said she had had sex with Mr Trump just once.
Mr Trump married Melania Trump in 2005.
She told the 60 Minutes show, which just aired in the US, that she had been approached by the man in the car park after having agreed to tell her story to a magazine.
"I was in a parking lot, going to a fitness class with my infant daughter," she said.
"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."
President Trump has not responded to the latest allegations.
He had been at his Mar-a-Lago estate in Florida over the weekend but was due to return to the White House ahead of the interview on 60 Minutes, the Washington Post has reported.
Mrs Trump, however, is staying in Florida, a White House spokeswoman said.
Ms Clifford is one of three women who have launched legal action over alleged affairs or sexual assault claims involving Mr Trump.
Her lawyer, Michael Avenatti, told the BBC that his client's case was different to others' because of "acts of intimidation and the tactics that have been used to silence my client".
"I think that is very problematic and it should be very disturbing to not only the American people but anyone in western civilisation," he added. "That is not how people in power should conduct themselves."
Ms Clifford says she was paid $130,000 by Mr Trump's personal lawyer, Michael Cohen, to remain silent about the affair just before the 2016 election.
Mr Cohen confirmed in February he had privately paid her the money but did not say what it was for.
He said last month that neither Mr Trump nor the Trump Organization were parties to the transaction.
Mr Cohen also denies ever threatening Ms Clifford, CBS News reports.