(CNN) - Deputy Attorney Rod Rosenstein is "conflicted" as the head of the Russia inquiry and may have to recuse himself if he witnessed President Donald Trump attempt to interfere with the investigation, according to a senior Senate Republican.
In a move that could add new pressure on Rosenstein, Sen. Lindsey Graham, a member of the Senate Judiciary Committee, told CNN Tuesday that he has written a letter questioning the deputy attorney general's role in charge of special counsel Robert Mueller's investigation.
He noted that Rosenstein may be a witness to the firing of former FBI Director James Comey, a matter that the Mueller team has been investigating for months to determine whether the president inappropriately sought to interfere with the Russia investigation.
"I think Rosenstein is conflicted," Graham told CNN. "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."
The comments come as Rosenstein already has faced sharp criticism from Trump and growing scrutiny from House Republicans, who have demanded a swath of documents while warning they may hold him in contempt of Congress if the Justice Department fails to fully comply. While Senate Republicans have largely shied away from that fight with Rosenstein, Graham's concerns could pick up steam in GOP circles as Republicans raise questions about how the Mueller investigation is being carried out.
In the May 31 letter, Graham noted that Trump initially relied on a Rosenstein memo from May 2017 as his justification for firing Comey. He asked Rosenstein if he considers himself a "potential witness" regarding the firing of Comey.
"If so, should you recuse yourself from further interactions with and oversight of the Mueller investigation?" Graham asked in the letter.
Justice officials could not immediately be reached for comment on the letter.
CNN reported in April that Rosenstein has been in consultation with the senior ethics adviser at the Justice Department about this issue and has followed that individual's advice.
"You know he's a fine man, very ethical, good guy, but we're going to have to play this thing straight," Graham said Tuesday in the Capitol. "And 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?'"
Graham on Tuesday also broke with Trump, who publicly berated Attorney General Jeff Sessions for recusing himself from overseeing the investigation into any potential collusion between the Trump campaign and Russia -- because Sessions played a major role in the Trump campaign. Graham said Sessions made the right call.
"I don't think there's any lawyer in the country that would advise Jeff Sessions not to recuse himself," Graham said. "I like Jeff. He serves at the pleasure of the President. Replacing Jeff Sessions would be chaos. But after Mueller does his job, then I think if he wants a different attorney general it would be easier to do."
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