(CNN) The Justice Department reaffirmed Wednesday that Deputy Attorney General Rod Rosenstein would step aside from overseeing the Russia investigation if necessary, according to a letter obtained by CNN, but a senior Republican senator is not satisfied.

On Tuesday, South Carolina GOP Sen. Lindsey Graham told CNN he believes Rosenstein is "conflicted" from overseeing special counsel Robert Mueller's work given his role in the firing of former FBI Director James Comey -- an issue of interest to the Mueller team as it determines whether the President inappropriately sought to interfere with the Russia investigation.

"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 CNN, who also sent Rosenstein a short letter last week posing questions about whether he needed to recuse from the investigation.

Assistant Attorney General Stephen Boyd wrote back in response Wednesday, reaffirming the department's general policy of not publicly commenting about any federal investigation, but also addressed the recusal issue.

"The Deputy Attorney General would recuse from all or part of any matter if recusal were deemed appropriate by Department officials who are informed about the matter," Boyd wrote. "Otherwise, he has a responsibility to fulfill his oath to well and faithfully execute the duties of his office."

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