After a meeting with Senate intelligence committee leaders on Capitol Hill Thursday, Rosenstein was asked by a Sinclair Broadcast Group
reporter whether he threatened to quit.
Rosenstein was involved in the firing earlier this week of Comey, having met with President Donald Trump and writing a memo on Comey's actions as FBI director.
Intelligence Chairman Richard Burr told reporters Comey did not come up in the meeting.
Burr said after their meeting that it was not his call on whether Rosenstein should be removed from overseeing the Russia investigation because of the Comey fiasco.
"We don't have the luxury of choosing who we work with," Burr said after their meeting.
Asked if he believed Trump when he claimed that Comey told him three times that he was not the subject of an FBI investigation, Burr said, "We can't comment on that. That's a conversation that supposedly happened between Director Comey and the President."
Burr, R-North Carolina, and vice chairman Mark Warner, D-Virginia, both left a hearing with acting FBI Director Andrew McCabe for the meeting.
Dana Boente, the acting director of DOJ's national security division, was also present.
Rosenstein has also expressed frustration at how the White House handled the Comey dismissal, and using his reputation as cover for how it was done, sources familiar with the matter tell CNN.
Vice President Mike Pence and deputy White House spokeswoman Sarah Huckabee Sanders on Wednesday repeatedly cited Rosenstein's memo on Comey recommending the FBI director's removal, leveraging his reputation and bipartisan Senate confirmation vote.
This story has been updated.