Michael Avenatti, lawyer of adult-film actress Stormy Daniels speaks to media as he exits the United States District Court Southern District of New York on May 30, 2018 in New York City.

Michael Avenatti, the lawyer for porn star Stormy Daniels, narrowed down his claim that President Donald Trump paid off women with hush money over sexual affairs from "multiple other women" to "three" ahead of the 2016 election.

The lawyer alleged that Trump and his then-attorney Michael Cohen used "hush money" to silence three women in addition to Daniels and Playboy playmate Karen McDougal, issuing the accusation in a Twitter post early Friday morning.

"Three additional women. All paid hush money through various means. Time for Michael Cohen and Donald Trump to come 100 percent clean with the American people. All the documents, all the tapes, NOW," said Avenatti, a strident Trump critic.

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Avenatti did not name the three women or offer further details. He claimed he received new information about the hush-money payments to women linked to Trump in a previous tweet, and told CNBC that Cohen and his lawyer Lanny Davis "have all the information and facts."

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. Trump's legal representatives maintain that he had no knowledge of any payments.

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 an 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. Trump's legal representatives say the tapes exonerate him, while his critics believe the opposite.

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.