The guilty plea explains that Cohen lied to Congressional committees about the Trump Organization's efforts during the presidential campaign to build a Trump Tower in Moscow.
Cohen told a NY court that he had made false statements to the Senate Select Committee on Intelligence about an aborted Trump organization real estate project in Russian Federation.
Cohen was interviewed in October last year behind closed doors by lawmakers conducting their own investigation into whether Mr Trump's campaign worked with Russian Federation to sway the U.S. election two years ago. Both men are caught up in Mueller's Russian Federation investigation over claims that they may have conspired with WikiLeaks while the organization was releasing emails and documents that painted a poor picture of Democrat Hillary Clinton during the 2016 presidential election. Mueller's is investigating "links and/or coordination between the Russian government and individuals associated with the campaign of President Donald Trump".
Cohen told told two congressional committees past year that the talks about the tower project ended that January, a lie he said was an act of loyalty to Trump.
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The timing was not lost on Trump's lawyer handling Mueller's criminal investigation.
As he left the White House shortly after the court proceeding concluded, Trump called Cohen "a weak person".
Cohen also told lawmakers he had had limited contact with Mr Trump about the project, when in fact it had been "more extensive". "Not running or building a building", Trump said.
Asked by reporters if she was concerned about Mr Cohen's plea, top House of Representatives Democrat Nancy Pelosi said, "Of course, he lied to the American people".
"Michael Cohen is lying and he's trying to get a reduced sentence for things that have nothing to do with me", the president said.
"But zero, I mean I will tell you right now, zero, I have nothing to do with Russian Federation", he said.
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"These false statements regarding the continued pursuit of a Moscow-Trump Tower deal during much of the presidential campaign only underscore the importance of a thorough investigation into any financial entanglement between Trump and Russian Federation", he said.
The nine-page charging document for Cohen traces the behind-the-scenes communication about the project that had been discussed more than 20 years ago. He told the court he had arranged those payments, created to keep the women quiet before the presidential vote, at Trump's direction. "Sentencing is set for December 12", said Guy Petrillo, another of Cohen's lawyers.
On Jan. 14, 2016, just weeks before the Republican party caucus in Iowa, Cohen emailed the office of Kremlin spokesman Dmitry Peskov asking for help getting the Trump Tower Moscow project off the ground.
Michael Cohen walks out of a federal court in NY after pleading guilty to lying to Congress over an aborted project to build a Trump Tower in Russian Federation.
He testified under oath that Trump had directed him to make hush money payments to adult-film actress Stormy Daniels and Playboy model Karen McDougal, contradicting Trump's previous claims that he was not aware of the pay-offs.
Neumeister reported from NY.
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Poroshenko had earlier said that he attempted to speak with Putin by phone, but the Russian leader refused to take his call. Major fighting ended with a 2015 ceasefire but deadly exchanges of fire are still frequent.