"Specifically now, and in light of learning, one that Michael was taping the president, two, that he doesn't have a tape of this, I would believe the president", he said.
However, Giuliani said he himself was "not allowed" to release the tapes, which include what he said were "183 unique conversations", citing rules concerning the audio, which was among the materials seized from Cohen's office, home and hotel in NY in April amid a criminal investigation of Cohen by the United States attorney's office for the Southern District of NY.
Giuliani's recent attacks against Cohen's character have been in stark contrast to his prior praise for Cohen.
Wallace acknowledged that Cohen's claim suggests that Trump lied about what he knew about the meeting, but he seemed to write off the possibility that the White House will face problematic new questions about the president's connection to Russian Federation.
CBS News' Elections and Survey's Director Anthony Salvanto reports that this speaks to how Trump's strongest backers feel such a personal connection with the president and want to defend him against what they perceive as being a politically motivated witch hunt.
He said he does think the rift will continue between Trump and Cohen, but he doesn't think the tape reveals criminal activity.
Thursday night's report by CNN said then-candidate Trump was told by his son that Russians were offering to help the Trump campaign by offering compromising information on Clinton. Cohen is facing a federal criminal investigation as well as legal scrutiny for NY taxicab companies he owns.
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He similarly told ABC News in early July, "I have no concerns that Michael Cohen is going to do anything but tell the truth".
Trump, who in the past has denied knowing about the meeting before it happened, also shot back at Cohen, who was once so loyal to Trump that he said he'd take a bullet for his boss.
"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 said.
This contradicts his earlier statement that called Cohen an "honest, honorable lawyer". Along with the testimony, the committee released emails from the president's son that showed him saying things such as "If it's what you say I love it" in response to an email offering dirt on his father's opponent, Hillary Clinton. He certainly wouldn't be the first president, if he did, who had done so.
Meanwhile, Trump's current attorney, former New York City Mayor Rudy Giuliani, has branded Cohen as a "liar" after a tape of him speaking to Trump about a hush payment to a former Playboy model.
"No defense lawyer would say that", Goldberg said.