(CNN) Deputy Attorney General Rod Rosenstein doesn't see a need at this point for a special prosecutor in the probe into Russian meddling in the 2016 election, people familiar with his thinking tell CNN.

Democratic lawmakers and others have pushed for the move in the wake of the controversy over President Donald Trump's firing of former FBI Director James Comey. Critics of the Trump administration's handling of the Russia investigation have long held the view that a special prosecutor is needed.

The investigation is led by Dana Boente, the US attorney in Alexandria, Va., who also serves as the head of national security prosecutions at Justice Department headquarters.

One source says Rosenstein isn't inclined to make a change unless the FBI investigation appears to be imperiled. And at this point, FBI officials are confident that the investigation is moving ahead, despite Comey's abrupt firing earlier this week.

Indeed, Rosenstein has privately vowed to lawmakers and staff that he plans to allow the bureau's investigation to move forward, uninhibited by pressures from the White House.

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