Adult film actress Stormy Daniels (Stephanie Clifford) and Michael Avenatti, attorney for Stormy Daniels, speak to the media after a hearing related to Michael Cohen.

Michael Avenatti, the lawyer for porn star Stormy Daniels, said Thursday that President Donald Trump and his then attorney Michael Cohen "conspired to pay off multiple other women" besides Daniels and a Playboy model before Election Day 2016 — and "also were concerned about a pregnancy."

"Cohen has evidence and info in his possession and it must be released to the public," Avenatti said in a Twitter post making that claim.

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Avenatti's bombshell allegation came after he received new evidence about hush-money payments to women linked to Trump, he said in a subsequent tweet.

Asked by CNBC about the details of that evidence, Avenatti replied that Cohen's lawyer "Lanny Davis and Michael Cohen have all the information and facts."

"They should release it now," said Avenatti, whose client Daniels says she had a one-night sexual tryst with Trump in 2006.

"And the public should demand it."

Prosecutors already are eyeing whether payouts made to two women who publicly claim they had sexual liaisons with Trump constituted violations of campaign finance law.

If Avenatti's claim is correct, prosecutors will have more instances to sift through for possible illegalities.

Avenatti's claim came two days after CNN aired a audio recording made by Cohen in September 2016 that reveals Cohen and Trump discussing buying the rights to Playboy model Karen McDougal's story from the publisher of the National Enquirer. McDougal claimed to have had an affair with Trump beginning in 2006.

The Trump-friendly Enquirer never ran her story. Trump's current lawyer Rudy Giuliani has said Trump and Cohen never followed through with the idea of buying the rights to McDougal's tale.

But the tape showed that Trump two months before his election had knowledge of the Enquirer's deal with McDougal, despite claims made by his spokeswoman closer to the election that "we have no knowledge of this."

Daniels was paid $130,000 by Cohen — who was later reimbursed by Trump — shortly before the presidential election in exchange for her silence about her alleged fling with Trump.

The nondisclosure agreement that Cohen negotiated with Daniels' prior attorney barred Daniels from disclosing "confidential information" about Trump — who was identified by a pseudonym.

Confidential information was defined by that agreement as including details of Trump's alleged sexual partners and sexual conduct, in addition to "paternity information" and "any alleged children."

Eleanor McManus, a spokeswoman for Davis, when asked about Avenatti's new claims, told CNBC, "Mr. Davis declined to comment understanding that [Avenatti] is in the middle of litigation."

Avenatti is representing Daniels in several pending legal actions, including a lawsuit against Cohen and Trump that seeks to void the nondisclosure agreement on the grounds that Trump never signed it.

The White House, which did not immediately respond to CNBC's request for comment on Avenatti's new statement, has denied Trump had sex with either Daniels or McDougal.

Giuliani, who did not immediately respond to a request for comment, took a shot at Avenatti on Twitter, saying, "Please be warned that [Avenatti] is becoming desperate since he is being ignored."

"The Cohen-Cuomo tape makes clear [Daniels'] claim is dead and with it [Avenati's] meal ticket. Most media now consider him too much of a proven liar to put on. Any reliance is gross negligence," Giuliani tweeted.

Giuliani was referring to a report in The Wall Street Journal that Cohen had secretly recorded a conversation with CNN journalist Chris Cuomo earlier this year in which Cohen, talking about the payment to Daniels, said, "I did it on my own."

Avenatti promptly fired back at Giuliani, the former New York mayor.

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Cohen is under criminal investigation by federal prosecutors in New York, who are probing his business dealings as well as the payments to Daniels and McDougal.

He has not been charged in that case.