Rudy Giuliani, President Donald Trump's personal lawyer, said Sunday that he wouldn't cooperate with an investigation by House Intelligence Committee chair Adam Schiff into Trump's contact with the Ukrainian president.

Giuliani sparred with host George Stephanopoulos on ABC's "This Week" after a week of major developments in Trump's Ukraine scandal.

House Democrats are zeroing in on Trump's inner circle as they pursue the impeachment inquiry after a bombshell whistleblower complaint centered on a call in which Trump repeatedly pressured Ukrainian President Volodymyr Zelensky to investigate former Vice President Joe Biden, a political rival for the 2020 presidential election.

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Rudy Giuliani, President Donald Trump's personal lawyer, said Sunday that he wouldn't cooperate with an investigation by House Intelligence Committee chair Adam Schiff into Trump's contact with the Ukrainian president.

Giuliani sparred with host George Stephanopoulos on ABC's "This Week" after a week of major developments after a bombshell whistleblower complaint was revealed that centered on a July 25 phone call between Trump and Ukrainian President Volodymyr Zelensky in which Trump repeatedly raised to Zelensky a potential investigation into former Vice President Joe Biden, a political rival for the 2020 presidential election.

Amid the growing details released by the administration, House Democrats are zeroing in on Trump's inner circle as they pursue the impeachment inquiry over allegations that Trump pressured foreign officials to investigate his potential 2020 Democratic opponent for his own political gain.

However, Giuliani pushed back on the growing scrutiny over Trump's inner circle, saying he "wouldn't cooperate" with Schiff.

"I wouldn't cooperate with Adam Schiff," Giuliani said, adding that he thinks the Democratic lawmaker should be "removed" and if he was replaced with a "neutral person," Giuliani would consider cooperating.

"So that's your answer, you're not going to cooperate?" Stephanopoulos asked.

"I didn't say that," the lawyer said. "I said I will considerate it."

"You said you wouldn't do it," Stephanopoulos replied. "You said you will not cooperate with Adam Schiff."

"I said I will consider it," Giuliani said.

Schiff pushed back on "This Week," saying the probe would continue despite the administration's attempts to dismiss and discredit the whistleblower.

"This whistleblower showed a lot of guts to come forward," Schiff said. "The fact that what the whistleblower related came from third parties doesn't make it less credible when that information is borne out."

Schiff said the whistleblower "has already been substantially corroborated," pointing to the similarities between the report and the memo released by the White House that detailed the call.

Read more: Here's the truth about the allegations involving Joe Biden's son and Ukraine drummed up by Trump and Rudy Giuliani

Giuliani and other members of Trump's inner circle came into the spotlight after a memo released by the White House quotes Trump urging Zelensky to launch an investigation and instructing him to speak with US Attorney General William Barr and Giuliani.

The scandal goes back to a New York Times story published May 1 that detailed both Bidens' ties to Ukraine and revealed that the former vice president had successfully gotten a Ukrainian prosecutor removed from office.

Trump and Giuliani have pushed claims for months that the former vice president bribed government officials in Ukraine to stifle investigations into Burisma, the gas company for which Hunter was a board member.

Giuliani has remained a central figure in the controversy as he has reportedly tried to meddle with foreign policy between the US and Ukraine and appeared frequently on cable-news shows to slam the Bidens and defend the president.