Washington (AFP) - Porn actress Stormy Daniels's attorney said Monday his client receives threats on a "near-hourly basis" -- the morning after she broke her silence on an alleged affair with US President Donald Trump.

Daniels told CBS's "60 Minutes" Sunday evening that she was approached by a man in a Las Vegas parking lot after she agreed to sell her story for $15,000 in 2011.

"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,'" she said.

When asked by CBS if he is worried for her safety, her lawyer Michael Avenatti replied, ""Absolutely."

"She receives threats on a near-hourly basis. Now, we don't have anything tying those to (Trump lawyer) Mr. Cohen or Mr. Trump, to be clear, but she's certainly scared for her safety and the safety of her family," he said.

Doing the rounds on the morning talk shows, Avenatti told CNN it was "fairly obvious" the threat in Las Vegas came from "someone associated with the Trump Organization."

Trump's personal lawyer Michael Cohen, who paid Daniels $130,000 as part of a non-disclosure agreement signed in 2016, reportedly sent Avenatti and Daniels a cease and desist order late Sunday after the highly anticipated CBS interview aired.

Asked about the letter, Avenatti said, "This is a man who has a history of thuggish behavior using intimidation tactics trying to step on little people,"

"If she's not telling the truth, let the president take to the podium and call her a liar," he later told NBC. "Let the president come forward and say it never happened. There is a reason why this $130,000 was paid."