President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's attorney Rudy Giuliani on Friday criticized Michael Cohen Michael Dean CohenA huge deal for campaign disclosure: Trump's tax records for Biden's medical records Our Constitution is under attack by Attorney General William Barr Eric Trump says he will comply with New York AG's subpoena only after Election Day MORE's lawyer Lanny Davis for representing an indicted Ukrainian with links to Russian President Vladimir Putin.

"Lanny Davis represents a gentleman named Firtash," Giuliani told Hill.TV's Buck Sexton on "Rising," referring to a Ukrainian oligarch.

Dmitry Firtash signed on to be represented by Davis's law firm, Davis Goldberg & Galper, in 2016.

"He is considered to be one of the close associates of [Semion] Mogilevich, who is the head of Russian organized crime, who is Putin's best friend. Lanny Davis has represented him for four or five years. If the newspapers are correct, he gets $80,000 a month from this guy who's considered to be one of the high-level, Russian organized crime members or associates," Giuliani said.

Davis said in a statement to Hill.TV that Giuliani was wrong, and that Firtash was innocent.

"I hate to dignify anything Mr. Giuliani says – he is so different than the man he was when he was mayor of New York. Dan Webb, a former U.S attorney from Chicago and I are both are criminal defense attorneys for Mr. Firtash, who is an innocent man," Davis said. "Aside from that, Mr. Giuliani gets everything wrong, which is his custom, as we’ve seen over and over again when he lies about Donald Trump.”

Firtash was indicted by the U.S. during the Obama administration for his alleged role in an international titanium scheme.

Giuliani's comments come amid concerns that Cohen lied to the House Oversight and Reform Committee during recent testimony.

Davis told The Hill that Cohen had asked his former attorney, Stephen Ryan, last year to inquire about a possible pardon. Cohen told the Oversight and Reform Committee he never sought a pardon from Trump.

"I can't go into the other conversations that I had because there may be an attorney-client privilege, but there's no doubt in my mind that he asked his lawyers, not just one, several, to come to the Trump team, and to ask us, will the president give a pardon, even though he had been told before that the president wouldn't," Giuliani said.

Davis, who is also an opinion contributor for The Hill, later told Hill.TV in a statement Monday that there was no conflict between what he said and what Cohen told lawmakers.

“Despite false assertions made by President Trump and his apologists, I did not contradict Mr. Cohen’s testimony," Davis said. "In fact, I confirmed the truth of his statement to many publications, which printed my comment, that Mr. Cohen never asked President Trump for a pardon."

Updated at 11:15 a.m. on Monday.

—Julia Manchester