Daniels alleges that the man approached her and demanded that she "leave Trump alone" and "forget the story".
"A sketch years later about a nonexistent man", Trump wrote on his Twitter page. "A total con job, playing the Fake News Media for Fools (but they know it!)".
Trump's comment accompanied the re-tweet of a Twitter user - "Deplorably Scottish" - who said the sketch resembled Daniels' ex-husband.
The actress Stephanie Clifford, who uses the stage name Stormy Daniels, performs at the Solid Gold Fort Lauderdale strip club on March 9, 2018 in Pompano Beach, Florida.
"Apparently the man who threatened Stormy Daniels has several Super Bowl rings and goes by the alias 'Tom Brady, ' " another person quipped. During a Tuesday appearance on "The View", she and her attorney, Michael Avenatti, also announced a $100,000 reward for information leading to the man.
Before the 2016 election, Trump's personal lawyer, Michael Cohen, admitted to paying Daniels $130,000 from his own pocket as part of a hush agreement.
Mr Avenatti gleefully welcomed Mr Trump's tweet.
"In my experience, there is nothing better in litigation than having a completely unhinged, undisciplined opponent who is prone to shooting himself in the foot", he tweeted.
"OMG I knew it had to be Tom Brady", joked radio host Ben Shapiro, while journalist Jemele Hill asked, "Uh is it just me or does he kind of look like Tom Brady?"
"I'm tired of being threatened, intimidating me, and trying to say that you'll ruin my life and take all my money and my house", Daniels said.
Daniels' sketch depicts a white male in his 30s or 40s and carries a description of him as "lean but fit".
Cohen and Trump have both blasted the FBI raid as a violation of attorney-client privilege.
The choice not to discipline Hannity frustrated some staffers.
Daniels recently unveiled a sketch of a man that she claims threatened her in Las Vegas about seven years ago. "Yes, there's a lot of publicity, but I didn't do it for that because this isn't what I want to be known for".
President Donald Trump shares a laugh with (clockwise from left) Ms.Seema Verma, Administrator of the Centers for Medicare and Medicaid Services, Secretary Tom Price, U.S. Secretary of Health and Human Services, and Vice President Mike Pence on.
Mr Cohen has threatened Daniels with up to $US20 million in damages for breaching the October 2016 nondisclosure agreement.
Mr Trump has largely remained quiet on the subject of Daniels, although he told reporters earlier this month that he did not know about the payment to the actress.
Daniels is also suing Mr Cohen for defamation and has sought to force the president to testify under oath.
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