Presidential attorney Rudy Giuliani dominated the Sunday political shows days after he said in an explosive interview that 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 reimbursed his personal attorney for a payment to adult-film actress Stormy Daniels.

Giuliani told ABC’s “This Week” that he recently joined Trump’s legal team to handle 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’s Russia investigation, but the focus Sunday remained on Michael Cohen’s payment to Daniels, whose real name is Stephanie Clifford.

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The renewed scrutiny over the Daniels controversy comes after Giuliani ignited a firestorm last week when he told Fox News’s Sean Hannity that Trump reimbursed Cohen for the payment to Daniels. Giuliani's statement contradicted a prior claim from the president, who said last month that he was not aware of the payment.

“The agreement with Michael Cohen, as far as I know, is a long-standing agreement that Michael Cohen takes care of situations like this then gets paid for them sometimes,” Giuliani said during his Sunday appearance on "This Week." “Sometimes it’s reimbursed in another way, depends on whether it’s business or personal.”

Giuliani insisted that Cohen made the payment for personal reasons and that it did not constitute a campaign contribution.

“Now this was for another purpose, to protect [Trump], to protect his family. It may have involved the campaign, doesn’t matter,” Giuliani said.

The former New York City mayor also reiterated his need to “focus [his] attention” on Mueller’s investigation, adding that Trump would not need to comply with a potential subpoena.

“He's the president of the United States. We can assert the same privilege as other presidents have,” Giuliani said. “President Clinton negotiated a deal in which he didn't admit the effectiveness of the subpoena.”

But Rep. Adam Schiff Adam Bennett SchiffChris Matthews ripped for complimenting Trump's 'true presidential behavior' on Ginsburg Trump casts doubt on Ginsburg statement, wonders if it was written by Schiff, Pelosi or Schumer Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence MORE (D-Calif.) argued that Trump would need to comply with a possible subpoena.

“No, he’s going to need to comply with a subpoena. If they take that case to court, they’re going to lose,” Schiff told CNN’s “State of the Union.”

Schiff, a frequent critic of Trump, said he has been “taken aback” by Giuliani’s legal strategy since joining Trump’s team, adding that his methods have been “deeply hurtful” to the president’s case.

“Notwithstanding the efforts of damage control, I think this is a very unpromising strategy,” Schiff said.

Attorney Alan Dershowitz echoed Schiff’s observation, telling NBC’s “Meet the Press” that Trump’s lawyers are playing into Mueller’s hands.

“It seems to me that the approach last week of the Trump team plays into the hands of Mueller’s tactic to try at any cost ... to find technical violations against lower-ranking people so that they can be squeezed,” Dershowitz, an opinion contributor for The Hill, said.

White House counselor to the president Kellyanne Conway Kellyanne Elizabeth ConwaySpecial counsel investigating DeVos for potential Hatch Act violation: report George and Kellyanne Conway honor Ginsburg Trump carries on with rally, unaware of Ginsburg's death MORE on Sunday sought to clarify Giuliani's apparent contradiction of Trump over the Daniels payment, arguing that the president meant he was not aware of the transaction at the time Cohen made the payment. Conway, during an appearance on CBS's "Face the Nation," also pushed back against Giuliani’s characterization of the payment as a campaign expenditure.

“I don't know why anyone would say that. I would not characterize it that way, the president himself characterized it as not a campaign expenditure,” Conway said.

“All I can tell you is that as the campaign manager for them, winning part of the campaign, this never crossed my desk.”

Giuliani has spoken to multiple news outlets in the days since his initial interview with Hannity, as he tries to mitigate the fallout from his comments.

His remarks have also put Daniels and her lawyer, Michael Avenatti, back in the spotlight. Avenatti said on ABC's "This Week" that he expects proof of other payments to emerge.

"Women have come forward and contacted our office ... as I’ve stated in the past. And we haven’t completed vetting those stories but I think at the end of the day, there’s going to be evidence of such payments," he said.

Giuliani, meanwhile, said Sunday that while he is not aware of any payments Cohen made to other women, he believes Trump’s personal lawyer would have done so if he deemed it “necessary.”

But Conway said during an interview with CNN’s “State of the Union” that she is also not aware of any additional payments.

“They didn’t cross my desk as campaign manager,” she said.