After Comey's firing Tuesday night, White House officials said President Donald Trump acted on the recommendation of Rosenstein.
Rosenstein told Sinclair Broadcast Group today, "No, I'm not quitting."
In a letter to staffers and friends after his firing, Comey said he was not going to dwell on how it was handled.
"I'm not going to spend time on the decision or the way it was executed. I hope you won't either. It is done," he wrote. "In times of turbulence, the American people should see the FBI as a rock of competence, honesty and independence."
The White House initially said Rosenstein's recommendation was the reason Trump fired Comey.
Press secretary Sean Spicer pointed the finger at the Justice Department when asked by ABC News late Tuesday night who ordered the review of Comey.
But Sanders said during Wednesday's White House press briefing, "The decision for the final decision to move forward with it was yesterday. But I know that [Trump has] been contemplating it for a while."
Asked whether Comey's firing was a result of Rosenstein's memo, Sanders said, "That was, I think, the final piece that moved the president to make that quick and decisive action yesterday."
Despite being critical of Comey for his handling of the Hillary Clinton email investigation, Democrats argued that the firing of Comey, who was overseeing the Russia investigation, is an abuse of presidential power.
"The reality is his team is the subject of an investigation," Adam Schiff, the ranking Democrat on the House Intelligence Committee, said in an interview with CNN Wednesday. "None of us know where that investigation is going to lead, and that's a very apparent conflict of interest for the president."
In his letter to Comey telling him he was terminated, Trump made a point of raising the FBI's Russia probe.
"I greatly appreciate you informing me, on three separate occasions, that I'm not under investigation," Trump wrote.
Associates of Comey's told ABC News they are highly skeptical that he would have told the president that he was not under investigation.
They said it's possible that was Trump's understanding but Comey never would have cleared anybody while an investigation is underway, adding that it would have been highly inappropriate for him to do so.