The news comes the same hour Mr. Trump's former campaign chairman, Paul Manafort, was also found guilty on eight counts - five counts of tax fraud, one count of failing to disclose a foreign bank account, and two counts of bank fraud.
In pleading guilty on Tuesday, Cohen stated that he made hush payments in 2016 to women who claimed to have had affairs with the Republican presidential nominee, and did so at the "direction of the candidate", plainly meaning Trump.
In another blow for the USA president, Paul Manafort, the man who once led Trump's election campaign in 2016, was found guilty of eight financial crimes.
Cohen, who was one of Trump's closest associates for more than a decade, said in court that he arranged to make payments "for (the) principal goal of influencing (the) election" at the direction of a candidate for federal office. The 22-page plea deal admits this as a violation of campaign finance, as these expenses were not declared as such. He has called Cohen "a very talented lawyer" and, as recently as June, "a good person".
Despite Cohen's admission directly implicating the president in a federal crime, justice department guidelines prevent the president from being indicted.
Trump's own lawyer, Rudy Giuliani, has dismissed Cohen and Davis' accusations, saying there "is no allegation of any wrongdoing against the President in the government's charges against Mr. Cohen".
Michael Cohen turned against Donald Trump after the President backed Vladimir Putin ahead of U.S. intelligence services.
In Manhattan federal court, Cohen pleaded guilty to eight counts in all, including tax evasion.
Trump defended Manafort, praising him in another tweet as "a fearless man".
Mr Trump said the Manafort case had nothing to do with the alleged 2016 collusion that Mr Mueller is probing and dismissed Michael Cohen's admissions.
Many legal and political observers expect Trump to eventually pardon Manafort, whose case was the first to be brought to trial by Robert Mueller, the former director of the Federal Bureau of Investigation, whose team repeatedly has been heavily criticized by the president.
Michael Cohen and Paul Manafort.
UPDATE: Fox News' Chief White House correspondent is reporting that Cohen's plea includes 3 to 5 years in prison.
It was the first trial victory for special counsel Robert Mueller's team.
Trump didn't mention Cohen at the West Virginia rally Tuesday night in Charleston for Republican Senate candidate Patrick Morrisey, but again denounced the Russian Federation inquiry and coverage by news media. "No collusion, no crime", she said on Twitter. Trump did not mention Manafort or Cohen during the rally, complaining only briefly about the "witch hunt", his favored term for Mueller's investigation into Russian interference.
The office of House Speaker Paul Ryan said it was "aware of Mr Cohen's guilty plea to these serious charges" but would need "more information" to be able to comment.
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