Sen. Lindsey Graham has become one of President Donald Trump's staunchest defenders on Capitol Hill.

But Graham – who sharply opposed Trump's decision to pull U.S. troops out of Syria this month – said in an interview with Axios that he will not support the president "at all costs."

And the South Carolina Republican who chairs the Senate Judiciary Committee did not rule out voting to convict Trump if he is impeached in the House and more evidence against him comes to light.

"Sure," Graham said when asked if there was anything that could persuade him to support Trump's impeachment. "Show me something that is a crime. If you could show me that Trump actually was engaging in a quid pro quo, outside the phone call, that would be very disturbing."

Trump is facing an impeachment inquiry centered on the allegation that he withheld military aid to Ukraine as leverage to prompt that country's new president, Volodymyr Zelensky, into investigating claims that former Vice President Joe Biden used his influence to oust a prosecutor who was looking into a company tied to Biden's son Hunter Biden.

More:How the Trump White House's messaging evolved on whether there was a Ukraine quid pro quo

But officials in the U.S. and Ukraine who have looked into the matter concluded neither Biden was guilty of any wrongdoing.

Trump also wanted Zelensky to look into a claim that Ukraine, not Russia, was behind the hack of the Democratic National Committee during the 2016 campaign and that a missing DNC server could offer proof. Trump's former homeland security adviser Thomas Bossert has said the idea is "a conspiracy theory" that has been "completely debunked."

One of the primary pieces of evidence that have been made public in the impeachment inquiry is a summary of a July 25 call between Trump and Zelensky in which Trump said he would need a "favor though" after Zelensky said he would like to buy more missiles from the U.S.

Graham has been highly critical of House Democrats' handling of the impeachment inquiry (calling it a "sham" and a "charade"), as he was of special counsel Robert Mueller's investigation. And he has consistently said he does not think the transcript of the July 25 call established proof of a "quid pro quo" tying the release of aid to the opening of investigations – though many congressional Democrats say the transcript itself proves Trump's guilt.

"The transcript speaks for itself – no quid pro quo," Graham tweeted Sept. 26.

That position conflicts with statements made by Acting White House Chief of Staff Mick Mulvaney, who told reporters last week that an investigation into Ukraine's role in the missing DNC server was one of the conditions that had to be met before the aid was released. He did not deny a quid pro quo and indicated he felt there would be nothing wrong if Trump had asked for one.

Mulvaney has since retracted those comments, telling Fox News' Chris Wallace on Sunday, "There was never any connection between the flow of money and the server."

Mulvaney said he "didn't speak clearly" and "folks misinterpreted what I said."

"You said what you said," Wallace told him.

Mulvaney's comments were made after Axios' interview with Graham, which was taped on Tuesday. But Axios reported that Graham's spokesman Kevin Bishop said on Friday that Graham "still has not heard or seen anything that he deems impeachable."

On Sunday, Graham told Fox News he supports Trump's call for an investigation into corruption in Ukraine that includes a look at 2016 election interference.

"I think Ukraine was involved in the 2016 election. I think they were trying to hurt Trump. They may have been working with the Democrats," Graham said on "Sunday Morning Futures."

He called for "somebody to look at Ukraine involvement in our 2016 election like Mueller looked at the Russian involvement."