Trump lawyer Rudy Giuliani told Reuters on Friday Cohen recorded a conversation with Trump in September, two months before the 2016 election, in which they discussed buying the rights to a story by a former Playboy model, Karen McDougal, who said she had an affair with Trump.
He added that there was some good news out of the debacle after all, "the good news is that your favourite President did nothing wrong!"
Cohen attorney Lanny Davis made a more subtle dig against Giuliani on Twitter Friday when he said that Cohen would not be "hurt" by the contents of the recording, despite attempts to "spin" what's on the tapes.
The prosecutors working on the case had not reviewed the recording because it, along with millions of other documents and files seized in Federal Bureau of Investigation searches of Cohen's home, hotel room and office in April, was undergoing the special master process, in which an independent party reviews whether the items should be regarded as privileged and thus withheld from prosecutors.
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White House press secretary Sarah Sanders later clarified that the president had said "No" to taking questions, and not the one about continued Russian interference.
Trump had initially said publicly that he believed his longtime fixer would remain loyal to him, but Cohen has increasingly suggested he's preparing to cooperate with the feds as he grows more and more isolated from his former boss.
Although Trump charged in his tweet that the Federal Bureau of Investigation broke into Cohen's office, the agency was executing court-approved warrants in conducting the searches. Michael Cohen, the man who once said he'd be willing to take a bullet for Donald Trump, has now provided perhaps the strongest evidence against him. NY state, for example, has a "one-party consent" law, which makes it a crime to record an in-person or telephone conversation unless one party participating in the conversation consents. Trump's campaign had said it knew nothing about any payment to McDougal, the former Playboy centerfold.
On the tape, the existence of which was revealed by The New York Times, Mr Trump was recorded talking about payments to Ms McDougal.
Trump had apparently been unaware of the recordings until he was told about them earlier this week.
Both Daniels and McDougal allege they had affairs with Trump around the same time, in 2006. At the time, Trump campaign spokeswoman Hope Hicks called McDougal's claims "totally untrue".
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The story in the July 30 edition of Time delves into the fallout from the Helsinki summit and Trump's seeming affinity for Putin. She said the USA hopes Putin will have the indicted Russians "come to the United States to prove their innocence or guilt".
Cohen had made a practice of recording conversations, unbeknownst to those he was speaking with. It is the client who owns the privilege and not the lawyer. "Any attempt at spin cannot change what is on the tape".
She claims they had a months-long affair in 2006, shortly after Mr Trump's wife Melania gave birth to Barron, their son.
"It's pretty clear from the tape, it's the first time Trump is finding out".
Federal prosecutors in NY have been investigating whether Cohen's actions, including a payment to adult film star Stormy Daniels, violated campaign-finance laws as part of a wide-ranging corruption probe into the longtime Trump fixer. But the tabloid did not publish the story, keeping it out of public view.
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Instead, he called the summit a "great success" and said he was looking forward to the second meeting. Our lawyers and diplomats should use this confession while preparing suits in global courts.