President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE’s lawyer Rudy Giuliani said Sunday that he wants a thorough investigation into the origins of 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 investigation of possible ties between the Trump campaign and Russia.

"It's crying out for someone to investigate the investigators. There should be a full and complete [inspector general] report and grand jury investigation of what happened here, after it became the Russia probe," Giuliani told CBS’s "Face the Nation." "What was the purpose of it? What did they gather?"

Giuliani pointed to "troubling unethical behavior" among some Justice Department (DOJ) officials that he said had tainted Muller’s probe.

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“I believe that the Mueller investigation should be investigated, not because necessarily of Mueller, but because of its genesis in this very, very now completely almost illegal and unethical probe, this Russian probe, that began with Peter Strzok in charge,” Giuliani said on CNN’s “State of the Union.”

“I don't think Mueller and his people need to be investigated unless something comes out of that,” Giuliani added.

Giuliani, in particular, homed in on an inflammatory text message exchange sent between two FBI officials, counterintelligence agent Peter Strzok and FBI lawyer Lisa Page, which were revealed in a report from the DOJ's internal watchdog last week.

In the exchange, Strzok told Page he "might be willing" to take action to stop then-GOP presidential candidate Trump from winning the election.

According to the report, Strzok told Page in a text message “we'll stop it,” after Page asked, "[Trump's] not ever going to become president, right? Right?!"

Strzok, who oversaw the investigation into former Secretary of State Hillary Clinton Hillary Diane Rodham ClintonDemocratic groups using Bloomberg money to launch M in Spanish language ads in Florida The Hill's Campaign Report: Presidential polls tighten weeks out from Election Day More than 50 Latino faith leaders endorse Biden MORE's use of a private email server, was later removed from Mueller’s investigation.

"How much did he infect that probe with his own very, very extreme positions? I don't know, but I want to find out before I go forward," Giuliani said when pressed about Strzok.

The inspector general's report concluded that there was no evidence that the conduct or potential political bias of Strzok and Page "directly affected the specific investigative actions we reviewed."

Giuliani called for Mueller to suspend his investigation after Inspector General Michael Horowitz released his highly anticipated report on Thursday.

The next day, Giuliani reiterated that the investigation should be suspended but said there should also be an investigation into Mueller’s probe.

“That kind of investigation should not go forward,” he said. “It’s time for Justice to investigate the investigators.”

Giuliani and Trump have been frequent critics of the special counsel's probe, often calling for its conclusion and seeking to undermine its legitimacy. The two have dubbed Mueller's investigation a "witch hunt" on numerous occasions.

Mueller is reportedly seeking to conclude the investigation this summer, according to The Washington Post.