Giuliani's comments came after Cohen reportedly claimed that he was there when Donald Trump Jr. informed Trump of a Russian offer to share dirt on Hillary Clinton.
Mr Trump, his son, his lawyers and other administration officials have repeatedly said Mr Trump did not know about the meeting until news of it broke in July 2017.
President Donald Trump's former lawyer has said his client knew in advance of a June 2016 meeting between his aides and a Russian delegation that offered to help his campaign, USA media report.
Rudolph Giuliani, one of the president's private attorneys with regard to the Russian Federation investigation, told NPR on Thursday that the CNN report was not true and labeled Cohen the "liar in chief". "I would not accept him in a case as a witness, as a prosecutor", he added later.
Trump's son-in-law Jared Kushner, son Donald Jr., and top campaign official Paul Manafort met at New York's Trump Tower on June 9, 2016 with Russian lawyer Natalia Veselnitskaya, who had said she was offering information from the Russian government aimed at helping Trump win the presidency.
In another tweet, he again denied any collusion with Moscow and denounced the Mueller probe as a witch hunt.
Cohen is right, this also means that Don Jr. perjured himself in his testimony to Congress. Perjury is a crime-a crime that got Bill Clinton impeached.
'Blood moon' to appear for 21st Century's longest lunar eclipse
For those in North America, the century's longer lunar eclipse will not be visible as it will take place during the day on Friday. Even if there was no organic material on the moon during those years, they were periods of intense meteoric activity.
Michael Cohen is turning into a risky adversary for the U.S. president.
Three days after Cohen's new lawyer, Lanny Davis, released a tape of Cohen and Trump talking about paying for Playboy model Karen McDougal's silence, the relationship splintered further Friday.
Rudy Giuliani just went on CNN to claim we can't trust the words of Michael Cohen, a "known liar". "We are very confident of the accuracy and reliability of the information that has been provided by Mr. Trump, Jr., and on his behalf".
But amid all of the questions about who knows what, here's what we know about the Trump Tower meeting? Trump has denied having had an encounter with Daniels.
Alan Futerfas, a lawyer for Donald Trump Jr., said the president's son stands by previous denials of his father's knowledge of the meeting.
Cohen's camp has denied being the source of the CNN report, the basic substance of which The Associated Press independently confirmed. He now seems to be pointing a gun at Mr Trump's head. "A particular focus will be Trump Jr.'s initial statement about the meeting, which turned out to be false, and which the president dictated from Air Force One while returning from Europe".