Harder did not immediately respond to CNBC's inquiries about Trump's tweet from Tuesday morning.
Just a few weeks before the 2016 presidential election, Trump's former personal lawyer Michael Cohen coordinated a $130,000 hush-money deal to keep Daniels silent about the alleged affair.
Daniels, represented by Avenatti, is suing Trump and Cohen to void that nondisclosure agreement, which she says was never validated because Trump himself never signed it.
Cohen has since pleaded guilty to campaign finance violations. He admitted to making payments to two women at the direction of an unidentified federal candidate for political office intended to influence the outcome of the election.
While Cohen didn't name Trump directly during the hearing, his attorney Lanny Davis said shortly afterward that "Donald Trump directed [Cohen] to commit a crime by making payments to two women for the principal purpose of influencing an election."
Avenatti stayed on the attack against Trump in a follow-up tweet, referencing his recent speech before the United Nations in New York City, in which Trump drew laughter from the crowd of national representatives for his assertion that his administration "has accomplished more than almost any administration in the history of our country."
Avenatti recently said he is "exploring" a presidential run and has begun speaking at Democratic Party events. In the meantime, he has quickly established himself as one of Trump's most vocal critics.
He waded into Supreme Court Justice Brett Kavanaugh's politically fraught confirmation battle in September when his client, Julie Swetnick, accused Kavanaugh and others of spiking girls' drinks at parties to make it easier for them to be gang raped.
Kavanaugh vehemently denied the allegations, saying they were "from the Twilight Zone." After the FBI opened a supplemental probe into numerous allegations of sexual misconduct against Kavanaugh, Avenatti complained that Swetnick was not interviewed by the bureau.
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