Daniels, 39, whose real name is Stephanie Clifford, allegedly had an affair with Trump more than a decade ago.
During the interview with Anderson Cooper, she alleged she had unprotected sex with Trump and spanked him with a magazine even although she was not "physically attracted" to him.
She told Cooper: "He was like, 'Wow, you — you are special. You remind me of my daughter."
"He was like, 'You're smart and beautiful, and a woman to be reckoned with, and I like you. I like you.'"
Daniels said Trump reportedly told her not to worry about his wife, Melania, who had just given birth to their son, Barron.
She also alleged that the President would phone her often and said he would try and get her on his show Celebrity Apprentice.
However, she refused to say whether she had any texts or photographic evidence of their alleged relationship.
Last week Playboy Playmate Karen McDougal said she had an affair with Trump.
The president's attorneys claim Daniels is liable for more than $20 million in damages for violations of an agreement she signed.
Daniels' attorney, Michael Avenatti, tweeted on Sunday that the interview was just the beginning of the saga, and hinted that more evidence will be released.
It has been reported she received $130,000 from Trump's attorney, Michael Cohen, as part of a hush agreement just before the 2016 presidential election.
This was the first time she has appeared on television to talk about the alleged affair.
President Trump returned to Washington from Palm Beach on Sunday while his wife Melania stayed in Florida on a pre-scheduled spring break.
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