Also, ousted FBI Director James Comey had said at a CNN town hall in April that collusion was "not actually a thing that exists under the federal laws of the United States", adding that conspiring with a foreign government to commit crimes against the U.S. was a crime.
Trump launched his new attack hours before his former campaign chairman, Paul Manafort, was due to go on trial on tax and bank fraud charges in Virginia.
'So I said today that there was no collusion therefore - and that collusion also is no crime. Asked about what specific conflict the president was referring to in a Monday interview with CNN, Trump's personal attorney Rudy Giuliani described it as a "dispute" but left it to the president to further characterize his complaint.
In his tweets, Mr Trump also said the investigation was triggered by a damning dossier compiled by former British intelligence agent Christopher Steele, and questioned why Mr Mueller was not probing Democrats.
File photo of USA president Donald Trump.
On Monday, Giuliani called on Mueller to "be a man" and disclose the alleged conflict of interest, though the former New York City mayor said he wasn't aware of what it was.
As part of her opening monologue on Monday night's Unfiltered, the HLN host recapped the latest revelations from Cohen - noting that he's come a long way from the days where he professed his absolute loyalty to the president.
Giuliani also sent a message to Mueller: It's time for the special counsel to "put up or shut up". The President has said he would like to sit down with Mueller if he perceived he would be treated fairly.
He provided no evidence that the team led by Mueller, a Republican appointed by Republicans, is biased against him.
In the CNN interview, Giuliani referenced a conflict so severe that if it were him, 'it's one that would have kept me out of the investigation.' But he wouldn't divulge more.
In a series of tweets targeting Mr Mueller's credibility, Mr Trump alleged he had "a very nasty and contentious business relationship" with Mr Mueller.
Trump fumed about what he claimed were conflicts of interest on Twitter Sunday.
Russian Federation has denied the finding of USA intelligence agencies past year that it interfered to sway the election to Trump.
Giuliani also said it "sounds suspicious" that only one of 183 Cohen recordings obtained from Federal Bureau of Investigation raids on his home and office has Trump on it. Only 1 with the president of the united States, ' Giuliani said.