President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE's personal lawyer Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE on Sunday called House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffSchiff to subpoena top DHS official, alleges whistleblower deposition is being stonewalled Schiff claims DHS is blocking whistleblower's access to records before testimony GOP lawmakers distance themselves from Trump comments on transfer of power MORE (D-Calif.) "an illegitimate chairman" but said he would testify before Congress if instructed to do so by President Trump.

Giuliani told George Stephanopoulos George Robert StephanopoulosColbert implores Pelosi to update 'weaponry' in SCOTUS fight: 'Trump has a literal heat ray' Murkowski: Supreme Court nominee should not be taken up before election Cruz says Senate Republicans likely have votes to confirm Trump Supreme Court nominee MORE on ABC's "This Week" that he will "be guided by my client."

ADVERTISEMENT

"I'm a lawyer," he said. "It's his privilege, not mine. If he decides that he wants me to testify, of course I'll testify."

Giuliani added that he thought Schiff should be removed from his committee post.

"He has already prejudged the case," Giuliani said. "If we want fairness here, we've got to put somebody in charge of that committee who has an open mind, not someone who wants to hang the president."

NEW: Asked repeatedly if he would cooperate with House Intelligence Committee, Rudy Giuliani tells @ThisWeekABC, "I wouldn't cooperate with Adam Schiff," but then says he would "consider" it were chair Adam Schiff removed. https://t.co/S0bTTE1vKj pic.twitter.com/gszI6zeRUV — This Week (@ThisWeekABC) September 29, 2019

Giuliani's appearance, during which he often sparred with Stephanopoulos, came after a whistleblower report released last week regarding the Trump's call with the Ukrainian president put Trump and his lawyer under scrutiny.

The whistleblower report says Trump asked Ukrainian President Volodymyr Zelensky to "look into" former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE's son and offered to connect Zelensky with Giuliani.

The House has since started an impeachment inquiry.