Presidential attorney Rudy Giuliani made his rounds on the Sunday morning political shows, railing against 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 probe into Russia’s election meddling.

Giuliani, a former New York City mayor who joined 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 legal team last month, slammed the basis for which Mueller was appointed as special counsel as “illegitimate.”

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“I'm not saying Mueller is illegitimate,” Giuliani told CNN’s “State of the Union.” “I'm saying the basis on which he was appointed is illegitimate.”

The remarks from Giuliani come as the president continues to promote an unfounded claim that the FBI spied on his campaign using an embedded informant.

“With Spies, or ‘Informants’ as the Democrats like to call them because it sounds less sinister (but it’s not), all over my campaign, even from a very early date, why didn’t the crooked highest levels of the FBI or ‘Justice’ contact me to tell me of the phony Russia problem?” Trump wrote on Twitter Saturday.

Giuliani referenced the alleged spying in both of his Sunday show interviews, but told "Fox News Sunday" that it predated Mueller’s appointment.

“But it completely changed his investigation,” he told Fox guest host Bill Hemmer of the alleged spying.

Giuliani since joining the president’s legal team has grappled with the possibility of a sit-down interview between Mueller and Trump.

On Sunday, Giuliani once again said he won’t allow Trump to take part in a sit-down that could be a "trap for perjury," but provided mixed signals as to whether or not Trump will ultimately participate in an interview with Mueller.

“I mean, the reality is, we’re not going to sit him down if this is a trap for perjury,” Giuliani told Fox.

“He wants to explain that he did nothing wrong. It’s us, the lawyers, who have to convince him that this is a trap,” he added.

Echoing Trump, Giuliani said the investigation has been “rigged” against Trump.

Still, he said Trump won’t fire anyone to end the probe, for fear of comparisons to the Nixon-era Watergate scandal.

“They’re the people who have committed the crimes,” he said, referring to the FBI.

The comment is a reference to former President Nixon’s call to fire special counsel Archibald Cox, a request that became known as the “Saturday Night Massacre” because two Justice Department officials resigned rather than execute Nixon’s order.

Lawmakers on both sides of the aisle have expressed fears that Trump could fire Mueller or Deputy Attorney General Rod Rosenstein Rod RosensteinDOJ kept investigators from completing probe of Trump ties to Russia: report Five takeaways from final Senate Intel Russia report FBI officials hid copies of Russia probe documents fearing Trump interference: book MORE, who appointed Mueller.

Democratic lawmakers in recent days have criticized the president for claiming an informant spied on his campaign, noting there is no evidence to back up Trump's assertion.

"There is no evidence to support that spy theory," 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.), the ranking member of the House Intelligence Committee, told ABC's "This Week."

"This is just a piece of propaganda the president wants to put out and repeat. And certainly we've seen this pattern before."

Sen. Marco Rubio Marco Antonio RubioOvernight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers Democrats step up hardball tactics as Supreme Court fight heats up Press: Notorious RBG vs Notorious GOP MORE (R-Fla.) in his own Sunday show appearances defended the FBI, though he did not directly answer questions on ABC as to whether Trump’s claims about an informant were false.

“As far as what I have seen to date, it appears that there was an investigation not of the campaign but of certain individuals who have a history that we should be suspicious of that predate the presidential campaign of 2015, 2016,” Rubio told ABC.

“And when individuals like that are in the orbit of a major political campaign in America, the FBI, who is in charge of counterintelligence investigations, should look at people like that.”

The Florida Republican told CBS’s “Face the Nation” in a separate interview that he has yet to see evidence supporting Trump’s claim that there was an informant sent to spy on his campaign.

“What I have seen so far is an FBI effort to learn more about individuals with a history of bragging about links to Russia that pre-exist the campaign,” he said.

“If those people were operating near my office or my campaign, I'd want them investigated and I’d want to know about them. That's what I've seen so far.”