President Donald Trump's private lawyer is accusing his former counsel, Michael Cohen, of violating attorney-client privilege, ABC News reported on Saturday, cautioning him against making any more public disclosures about his dealings with the president.

Following a week of bombshell revelations, Rudy Giuliani, Trump's current attorney and the former New York City mayor, has demanded that Cohen and his lawyers "should respect the client and attorney privilege in different ways," Giuliani told ABC.

"We have complained to them that he's violated the attorney-client privilege, publicly and privately," Giuliani told ABC, adding that both camps were no longer sharing information as part of a joint defense agreement.

Trump has personally taken aim at Cohen for secretly recording their conversations, suggesting that doing so may have been illegal. However, it was Trump's legal team that actually waived protections that would have allowed the recordings to remain hidden from prosecutors, a source familiar with the matter told CNBC last week.

The former mayor's remarks drew a biting reply from Cohen's attorney, Lanny Davis, who himself is a well-renowned political fixer.

"Mr. Giuliani seems to be confused. He expressly waived attorney client privilege last week and repeatedly and inaccurately — as proven by the tape — talked and talked about the recording, forfeiting all confidentiality," Davis told CNBC in a statement.

Since Trump hired Giuliani in April, his defense of the president has come under increasingly withering criticism as the stakes in Special Counsel Robert Mueller's probe have gotten higher. In his initial weeks as Trump's legal counsel, Giuliani made an appearance on Fox News, where he famously revealed that Trump reimbursed Cohen for hush money paid to Stormy Daniels, a porn actress who claimed she had an affair with Trump before his election.