The president also distanced himself from Mr Cohen, who is now under federal investigation for possible campaign finance law violations in the Daniels matter as well as personal business activities, saying Mr Cohen did only a "tiny, tiny fraction" of Mr Trump's legal work and that his business activities don't have "anything to do with" the president.
Trump says "no campaign funds" were used and says Cohen was being investigated over his business. He has got a business.
Instead, Mr Trump veered immediately toward the witch hunt, the fix, the "phony cloud" that he says is hanging over his presidency in the form of the ongoing investigation into possible ties between his campaign and Russian Federation.
"Michael is in business, he is really a businessman, at fairly big businesses, I understand", Trump said.
And asked how much of his legal work Cohen is responsible for, Trump said: "As a percentage of my overall legal work, a tiny, tiny fraction".
Jones' role as special master means she will search through the documents, cell phone records, audio recordings, emails and computer records seized by the Federal Bureau of Investigation and determine which documents are covered by Cohen's attorney-client privilege - both for Cohen as a client and as an attorney. "And from what I see, he did absolutely nothing wrong". The payments are a central focus of a criminal probe launched by NY prosecutors against Cohen, which became public after Federal Bureau of Investigation agents raided Cohen's home, offices and hotel room earlier this month.
From there, Trump jumped to slamming the former Federal Bureau of Investigation director James Comey as a "leaker" and a "liar", before pivoting to slamming CNN as "fake news" and accusing the Justice Department - which is led by his political appointees - of not "doing their job".
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Thursday's comments are the first time Trump has publicly acknowledged that Cohen is representing him in the Daniels case.
"He did an illegal act, and he said it himself, in order to get a special counsel against me", the president said.
Lawyers for Trump and Cohen have sought to restrict what prosecutors are able to review based on a claim of attorney-client privilege. "I have nothing to do with his business".
Cohen is also dealing with a civil case filed by Daniels, who is seeking to invalidate the confidentiality agreement she signed before the election.
Despite its agreement to appoint a special master, prosecutors suggested a procedure that differs in significant ways from the proposals of Cohen and Trump. Daniels, whose real name is Stephanie Clifford, is suing Cohen for defamation for alleging that she lied about her affair with Trump.
Trump, who has reshaped his legal team while considering whether to be interviewed by special counsel Robert Mueller, called the investigation "a disgrace" and excoriated federal agents for executing search warrants on his longtime personal lawyer, Michael Cohen, and his onetime campaign chairman, Paul Manafort.
Saying he was "very disappointed in my Justice Department", Trump left the door open to changing his mind. Avenatti is petitioning to represent Daniels in the litigation over the materials seized from Cohen, since he says documents relating to Daniels are part of the seized information.