Sen. Lindsey Graham Lindsey Olin GrahamHarris slams Trump's Supreme Court pick as an attempt to 'destroy the Affordable Care Act' Sunday shows preview: Lawmakers prepare for SCOTUS confirmation hearings before election Confirmation hearing for Trump's Supreme Court pick to start Oct. 12 MORE (R-S.C.) warned on Wednesday that if Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE, President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE's personal lawyer, is going to publicly suggest a "cover-up" involving the Bidens and Ukraine "then I hope you know what you're talking about.”

Graham’s comments come after Giuliani took a trip to Ukraine this month and met with a host of former and current officials as part of an effort to unearth more dirt on Trump's political rivals, including 2020 presidential candidate Joe Biden Joe BidenBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Joe Biden should enact critical government reforms if he wins MORE.

Trump’s efforts to get Kyiv to announce investigations into the Biden family and unfounded accusations that Ukraine interfered in the 2016 elections are at the center of Democrats’ impeachment efforts against him.

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"I don't know what Rudy's got, but I'm going to send him a letter. If you're going to go on national television and tell the country that you've found evidence of a cover-up, then I hope you know what you're talking about,” Graham told reporters.

"I like Rudy a lot, but we're going to have to watch what we say,” he added.

Graham has invited Giuliani to testify before the Senate Judiciary Committee over his concerns about corruption in Ukraine. He reiterated on Wednesday that Trump’s lawyer has an “open invitation” before the panel he chairs.

"If he comes, you gotta be willing to ask questions about your conduct. It's just not good for the country to make these accusations on cable television without them being tested,” Graham added.

Giuliani told The Washington Post that Trump has asked him to brief GOP senators and the Justice Department on his findings in Ukraine. A source told The Wall Street Journal that Giuliani told the president that his recent trip produced "more than you can imagine."

Trump and his allies have latched onto Hunter Biden's connection to Ukraine, where he served on the board of an energy company, as the former vice president seeks the Democratic nomination to challenge Trump in 2020. There's no indication Joe Biden was acting with his son's interests in mind when he called for the ouster of a Ukrainian prosecutor accused of corruption, and the former vice president has denied any such motivations.