Cohen, who this week was sentenced to three years in prison, says he made the payments to help Trump's 2016 White House bid, a campaign finance violation.
The sentencing of Michael Cohen, President Donald Trump's former personal lawyer, brought a perilous investigation into the president's campaign one step closer to the Oval Office. Trump tweeted Thursday that Cohen, as a lawyer, gave him bad advice about the legality of the deals.
Cohen said in a guilty plea in August that he was directed by Trump to make hush money payments to two women - former Playboy model Karen McDougal and adult-film star Stormy Daniels - who said they had past sexual affairs with the president.
Federal prosecutors say the payments were made at Trump's direction. "That is why they get paid", he wrote.
In his three tweets on Thursday morning, local time, Trump made no mention of a cooperation deal announced on Thursday between federal prosecutors and the National Enquirer's parent company, in which it acknowledged paying money to McDougal to "suppress the woman's story" and "prevent it from influencing the election". After Cohen pleaded guilty to the Mueller charges on November 29, Trump called his former lawyer a liar, "a weak person and not a very smart person". It was because time and time again I felt it was my duty to cover up his dirty deeds rather than to listen to my own inner voice and my moral compass.
Cohen admitted charges brought by federal prosecutors in NY of tax evasion, providing false statements to a bank and illegal campaign contributions.
But the New York-based prosecutors who handled the case had urged the judge to sentence Cohen to a "substantial" prison term and said he failed to tell investigators everything he knows.
Cohen's crimes included evading $US1.4 million ($A1.9m) in taxes and misleading Congress about his talks with Russians about a Trump skyscraper project in Moscow. Cohen was guilty on many charges unrelated to me, but he plead to two campaign charges which were not criminal and of which he probably was not. The judge has ordered Cohen report to prison on March 6th.
Michael Avenatti, Daniels' lawyer, attended the sentencing and told reporters outside the courthouse, "Michael Cohen is neither a hero nor a patriot".
Trump this week sought to minimize the importance of the payments saying they were a "simple private transaction" and that they were "wrongly" being called campaign contributions.
Image copyright Getty Images Image caption Michael Cohen arrived for his sentencing with members of his family Who else has been implicated? We now have multiple witnesses saying Trump committed a felony to secure his election.
Donald Trump's former lawyer Michael Cohen had admitted to covering-up his "dirty deeds".
Another message from the fate of the two Trump associates is that Mr Trump's business dealings, not Russian election meddling, could present a greater legal threat to the president. They put that on to embarrass me....
For 12 years, Cohen was vice president of The Trump Organization, the umbrella company for Trump's real estate businesses, and one of the principal confidants of the NY billionaire.
Court documents allege that Cohen acted at the direction of Trump, who was a candidate for president at the time.
Although the founders included impeachment in the constitution as a political remedy, critics of the status quo have argued they never meant to give the executive a "free pass" for crimes just by holding office, including alleged crimes that helped a president obtain the White House.
In an interview with Reuters on Tuesday, Trump denied the payments to the women were campaign contributions.