WASHINGTON –

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.

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

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.

Senate Democrats welcomed the chance to question Giuliani under oath about his role in pressing Ukraine to investigate the Bidens.

"Democratic members have plenty of questions for Mr. Giuliani and this would give us an opportunity to help separate fact from fiction for the American people," Sen. Dianne Feinstein, the committee's top Democrat, said in a statement.

Giuliani, the former New York City mayor, was not immediately available for comment.

The House Intelligence Committee, which is leading the impeachment probe, subpoenaed Giuliani to provide documents on Sept 30.

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.