Graham extended the invitation during an interview with CBS, which is set to air on Sunday.
Speaking for Face the Nation, the Republican said that it remains unclear what Giuliani found during his investigations in the eastern European country, asserting that he is welcome to testify before the Senate Judiciary Committee, which Graham chairs.
“Well, I don’t know what he found, but if he wants to come the Judiciary Committee — Rudy, if you want to come and tell us what you found, I’ll be glad to talk to you,” Graham said, noting that he is not inviting the lawyer to testify in the impeachment trial.
“When it comes to impeachment, I want to base my decision on the record assembled in the House,” he said.
Graham asserted that he does not know what Giuliani “was up to when he was in Ukraine,” but suggested that he was willing to use his committee to further investigate former Vice President Joe Biden and his son, Hunter.
“We can look at what Rudy’s got and Joe Biden, Hunter Biden and anything else you want to look at after impeachment. But if Rudy wants to come to the Judiciary Committee and testify about what he found, he’s welcome to do so.”
Giuliani has become one of the central figures in the impeachment case against Trump. During the impeachment investigation, the lawyer went to Ukraine to meet with numerous current and former government officials in an attempt to seek more dirt on the Bidens and allegedly investigate corruption.
Democrats in the House of Representatives want to impeach Trump over obstruction of Congress and abuse of power. They claim that the president committed impeachable offenses by allegedly pressuring Ukrainian authorities to launch investigations into his political opponents, the Bidens among others.
According to an anonymous intelligence community official who blew the whistle on Trump’s alleged wrongdoing, the president withheld — and threatened to permanently cut — military aid to Ukraine, effectively inviting the corruption-ridden country to meddle in the 2020 presidential election.
According to documents released by the State Department following a lawsuit from American Oversight, Giuliani worked together with other Trump administration officials to ensure that the investigations are launched. According to the documents, Secretary of State Mike Pompeo is also implicated in the scandal.
The documents suggest that Giuliani and Pompeo coordinated, working to pressure Ukrainian authorities as Trump was withholding military aid. The duo also worked on ousting former United States Ambassador to Ukraine Marie Yovanovitch, according to the memos.