(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.

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