WASHINGTON (Reuters) - The Republican chairman of the U.S. Senate Judiciary Committee on Tuesday opened the door to a Senate investigation into unproven allegations regarding Ukraine raised by President Donald Trump’s personal lawyer Rudy Giuliani, inviting the attorney to testify.

FILE PHOTO: U.S. Senate Judiciary Committee Chairman Lindsey Graham (R-SC) holds a news conference to discuss immigration legislation and the U.S.-Mexico border on Capitol Hill in Washington, U.S., May 15, 2019. REUTERS/Jonathan Ernst

“It is time for the Senate to inquire about corruption and other improprieties involving Ukraine,” Senator Lindsey Graham said in a series of tweets, mentioning specifically the firing of Ukraine’s former prosecutor Viktor Shokin.

“Therefore I will offer to Mr. Giuliani the opportunity to come before the Senate Judiciary Committee to inform the committee of his concerns,” he said.

Democrats, eager for the chance to grill Giuliani, lost no time welcoming Graham’s move and called for the Trump lawyer to testify under oath.

“Good. I have questions,” Senator Kamala Harris, a Senate Judiciary member and 2020 Democratic presidential candidate, tweeted to Graham. Two other Democratic presidential hopefuls also sit on the committee: Cory Booker and Amy Klobuchar.

Senator Dianne Feinstein, the panel’s top Democrat, said Giuliani’s appearance would give Democrats an opportunity to “separate fact from fiction.”

Giuliani and his unsubstantiated allegations are central to the Democratic impeachment inquiry in the House of Representatives, which followed a July 25 phone call in which President Donald Trump pressed Ukraine President Volodymyr Zelenskiy to investigate 2020 Democratic presidential candidate Joe Biden and his son, Hunter.

Graham, a South Carolina Republican and close Trump ally, did not give specific dates for a potential Giuliani appearance or any other public hearings on the matter.

A former New York City mayor, Giuliani said he would like to appear before the Senate panel but needed to determine whether maintaining confidentiality as Trump’s lawyer would be an issue.

The House Intelligence Committee, which is leading the impeachment probe, has subpoenaed Giuliani to provide documents.

He and others have made unsubstantiated claims that when Joe Biden was vice president, he had a prosecutor fired to halt an investigation into a Ukrainian gas company that Hunter Biden was involved in between 2014 and 2018.

Biden has dismissed the allegations and no evidence has emerged to support them.