"If you're looking at obstruction of justice misconduct post-presidency, the Comey firing as being a form of obstruction of justice, then Rosenstein is a key witness in that and you can't be a witness and oversee the investigation," Graham told reporters on Tuesday

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Graham's comments come after he sent Rosenstein a letter, dated from late last month, questioning his role overseeing the investigation into Russia's election interference and potential collusion between the Trump campaign and Moscow.

"Do you consider yourself a potential witness in the Mueller investigation regarding the firing of Director Comey by President Trump?" Graham asked in the letter.

If the answer is yes, Graham then asked if Rosenstein believes he should step back from the Mueller probe.

Graham indicated on Tuesday that Rosenstein had not yet responded to his letter.

"He's a fine man, very ethical, good guy, but we're going to play this thing straight," Graham said. "Here's the question for Rosenstein, if you're going to be a fact witness as to why Comey was fired, how do you stay involved?"

"I was going to fire Comey. There's no good time to do it, by the way," he told NBC News last year, calling Comey a "showboat" and "grandstander."

Rosenstein has reportedly explored potentially stepping back from the Russia investigation.

CNN reported in April that Rosenstein consulted with ethics officials about his role. And sources told ABC News in June 2017 that Rosenstein raised the issue with Rachel Brand, who was the No. 3 Justice Department official at the time.

Rosenstein has emerged as a controversial figure in the Russia investigation.

He initially enraged Democrats for the memo he wrote on Comey. More recently, he's emerged as a top target for Trump and his conservative allies on Capitol Hill, some of whom have urged the president to fire the deputy attorney general.

"I am being investigated for firing the FBI Director by the man who told me to fire the FBI Director! Witch Hunt,” Trump said in a tweet about Rosenstein last year.

Trump reiterated on Tuesday that he would not have picked Sessions to be his attorney general if he had known that he was going to recuse himself.

"The Russian Witch Hunt Hoax continues, all because Jeff Sessions didn’t tell me he was going to recuse himself...I would have quickly picked someone else. So much time and money wasted, so many lives ruined...and Sessions knew better than most that there was No Collusion!" Trump said in a tweet.