Rudy Giuliani, former mayor of New York,at the Oval Office of the White House in Washington, D.C., U.S., on Monday, March 25, 2019.

Sen. Lindsey Graham, R-S.C., said Tuesday that he will invite President Donald Trump's personal lawyer, Rudy Giuliani, to testify before the Senate Judiciary Committee about allegations of corruption.

Giuliani, former mayor of New York, has been out front defending Trump, who is mired in an impeachment inquiry launched by House Democrats last month after a whistleblower's complaint accused the president of soliciting Ukraine's leader to investigate his possible 2020 election rival, former Vice President Joe Biden, and his son Hunter.

Giuliani, who was included in that complaint, has also been a leading voice lobbing unsubstantiated allegations of wrongdoing against the Bidens.

In response to the invitation, Giuliani told CNN, "Love Lindsey, but I am still a lawyer and I will have to deal with privilege."

Graham's announcement came shortly after the Trump administration blocked Gordon Sondland, U.S. ambassador to the European Union, from participating in a closed-door deposition before Democrat-led committees in the House.

Graham is one of the president's closest allies in Congress, though he had criticized the administration just a day earlier for announcing that U.S. troops would be withdrawn from northern Syria, giving Turkey a path to invade the area and attack anti-ISIS Kurdish forces.

The invitation to Giuliani, who has been derided by Democrats as a conspiracy theorist improperly acting as a shadow White House official in his pursuit of dirt on the Bidens, signals a new effort by Republicans to push back against the impeachment inquiry, which has become an increasing threat to Trump's political aims.

"Given the House of Representatives' behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine," Graham said in a trio of tweets Tuesday morning.

"Therefore I will offer to Mr. Giuliani the opportunity to come before the Senate Judiciary Committee to inform the committee of his concerns," Graham tweeted.

Graham TWEET 1

Graham TWEETS 2&3

A spokeswoman for Giuliani did not immediately respond to CNBC's inquiries about whether Trump's personal attorney had received an invitation from Graham yet, or whether he planned to accept the offer.

In another tweet, Graham added: "I'm tired of only hearing one side of the story. It's now time to give voice to everything Ukraine. Let the chips fall where they may!"

Graham TWEET

Sen. Dianne Feinstein, D-Calif., the Judiciary Committee's ranking member, said in a statement: "I welcome the opportunity to question Rudy Giuliani under oath about his role in seeking the Ukrainian government's assistance to investigate one of the president's political rivals. 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."

The whistleblower's complaint alleged that Giuliani was a "central figure" in the alleged effort to get Ukraine to investigate the Bidens. The complaint jolted dozens of Democrats, including House Speaker Nancy Pelosi, D-Calif., to support an impeachment inquiry.

The complaint also raised suspicions that Trump may have delayed hundreds of millions of dollars in military aid allocated to Ukraine, which were withheld for months without a clear explanation from the White House, in order to pressure Ukraine to investigate.

Those concerns have been voiced by Democratic lawmakers, but were also shared by U.S. diplomatic officials, according to text messages provided by former U.S. special envoy to Ukraine Kurt Volker last week.

Trump has maintained that there was no "quid pro quo" involved in his requests to Ukraine. He has repeatedly defended his call as "perfect" and has said it is his "duty" to ask other countries to investigate allegations of corruption.

On Thursday, the president took things a step further, openly calling on China to look into the Bidens, as well. A handful of Republican senators issued statements rebuking Trump after those remarks.

Giuliani, in various interviews with media outlets, has accused Biden of pressuring Ukraine when he was vice president to fire a prosecutor there in order to protect his son, who was on the board of Ukrainian natural gas company Burisma Holdings. That prosecutor was reportedly overseeing an investigation into the owner of Burisma.

Giuliani has accused Biden and his family of profiting off of his position in public office. But there's no clear evidence that Biden's actions as vice president were intended to help his son; many other nations had also called for the Ukrainian prosecutor's resignation.

Hunter Biden has not been accused of wrongdoing related to his work with the company.