Rudy Giuliani told The Hill on Thursday that the media ought to “calm down” in their coverage of money paid to Michael Cohen, 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 longtime personal attorney.

The former New York City mayor and recent addition to Trump's legal team said of the allegations swirling around Cohen, “It doesn’t involve us at all. There is no suggestion that it does.”

Asked directly if Trump had any awareness of Cohen allegedly selling access to him or his administration, Giuliani replied, “No, of course not.”

Cohen has been in the middle of a firestorm since Tuesday, when Michael Avenatti — the attorney for adult-film actress Stormy Daniels, who alleges she had an affair with Trump in 2006 — published a document purportedly outlining payments to Cohen.

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Those payments came from an investment firm connected with a Russian oligarch, as well as from major corporations, including drug company Novartis and AT&T.

The broad thrust of Avenatti’s claims was verified by several news organizations and in statements from some of the companies.

Novartis, for example, acknowledged paying $1.2 million to Cohen’s company, Essential Consultants LLC. In an email to employees on Thursday, Novartis CEO Vasant Narasimhan wrote, “We made a mistake entering into this engagement.”

Adding to the intrigue, the payments were made to the same shell company, Essential Consulting LLC, that Cohen used to make a $130,000 payment to Daniels.

Cohen denies any wrongdoing.

Since the allegations came to light, Trump critics including Avenatti have insisted that the cloud of suspicion hovers over the president, too.

Avenatti told The Hill in a phone interview on Wednesday that the allegations “appear to reflect a pattern and practice by Michael Cohen of accepting money in return for access to the president.”

Avenatti added: “It’s beyond that it doesn’t look good. This is the right-hand attorney of the president. If that attorney is selling access to the president without the requisite disclosures, that is a serious problem.”

A CNN report on Thursday morning quoted an unnamed GOP strategist describing Cohen’s pitch to potential clients after Trump’s election in November 2016.

"I don't know who's been representing you, but you should fire them all. I'm the guy you should hire. I'm closest to the President. I'm his personal lawyer,” CNN quoted the strategist, apparently paraphrasing Cohen.

Giuliani pushed back against the coverage, saying Cohen’s consulting work did not touch the president at all.

“There is a sort of media frenzy about it. They ought to calm down. It doesn’t have any connection” to Trump, Giuliani said. “The main thing is, we are not involved.”

Asked if he had spoken to Trump about the latest twists and turns in the Cohen saga, Giuliani said, “I haven’t in a few days. He’s been very busy.”

Trump, on Tuesday, withdrew from the Iran nuclear deal, and then on Wednesday announced the release of three American hostages by North Korea as the details were finalized for a summit next month with North Korean leader Kim Jong Un.

Referring to the specifics of the Cohen case, Giuliani also said: “No one has told us what the details of that are, and on the face of it, it is hard to tell. Nobody is suggesting they were illegal. They might have been bad judgment, but even that is not clear.”

Giuliani himself was also in the news on Thursday, as he officially left his law firm Greenberg Traurig, from which he had previously taken a leave of absence to work for the president.

The former New York City mayor, in a statement from the law firm, explained his departure as coming “in light of the pressing demands of the Mueller investigation” and so that his “sole concentration can be on this critically important matter for our country.”

But the firm itself indicated that its executives have been discomfited by some of Giuliani’s public statements.

In a headlining-making interview with Sean Hannity of Fox News Channel last week, Giuliani had suggested that payments of the kind Cohen apparently made to Daniels were commonplace.

“Michael would take care of things like this like I take care of this with my clients,” he told Hannity.

On Thursday, a Greenberg Traurig spokeswoman told The New York Times, “Speaking for ourselves, we would not condone payments of the nature alleged to have been made or otherwise without the knowledge and direction of a client.”

Allies of Giuliani sought to cast his departure from the firm in much more positive terms.

One such ally told The Hill that his resignation showed he was “all-in as far as the Team Trump aspect of this is concerned.”

That source also speculated that, once the Russia probe led by special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE is over, “Rudy’s longer-term plan is to do something within the government — something Cabinet-level or even in the West Wing.”

Giuliani was added to the Trump legal team last month, ostensibly to help negotiate whether or not the president would agree to a voluntary interview with Mueller.

Asked for the latest thinking on that potential interview, Giuliani told The Hill: “We’re internally discussing it — but nothing we’re ready to talk about.”