Senate Republicans are hosting their own challenge to the House Democrats’ impeachment inquiry by inviting President Trump’s personal attorney Rudolph W. Giuliani to come testify on Ukraine, Sen. Lindsey Graham announced Tuesday morning.

Mr. Graham, chairman of the Senate Judiciary Committee, said he plans on allowing Mr. Giuliani to come before his committee to discuss the “disturbing allegations” about corruption in Ukraine and “many improprieties surrounding the firing of former Prosecutor General Viktor Shokin.”

“Given the House of Representatives’ behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine,” the senator tweeted.

Sen. Dianne Feinstein, the top ranking Democrat on the Judiciary Committee, said she would love the chance to ask Mr. Giuliani about the role he played 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,” she said in a statement.

House Democrats are centering their impeachment inquiry on allegations that Mr. Trump and his officials attempted to pressure Ukraine into opening an investigation into the Biden family.

Republicans are defending the president’s actions — arguing there should be an investigation into the allegations surrounding former Vice President Joseph R. Biden and the business dealings of his son Hunter.

They’ve also taken to slamming the Democrats’ entire process as a sham investigation — demanding that House Speaker Nancy Pelosi suspend the inquiry until the House holds a formal vote to authorize and establish equal power among the parties.

Mr. Giuliani has also been subpoenaed by the House Democrats as part of their impeachment investigation.

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