Rosenstein, who appointed Mueller as special counsel overseeing the probe into Russia's meddling in the 2016 election, deflected the question in a House committee hearing Tuesday afternoon.
"I am not at liberty to talk about that now, and the reason for that is that if it is within the scope of Director Mueller's investigation ... we don't want people talking publicly about open investigations," he said.
Rosenstein added that he has "no reservations about my role" in Comey's dismissal. But his comment left open the possibility that the investigation does cover the chain of events that led to Trump firing Comey.
Rosenstein said he is leaving to Mueller decisions about what the investigation covers.
In an earlier hearing Tuesday before a Senate appropriations subcommittee, Rosenstein said Mueller will have the "full independence he needs to conduct that investigation," and that he has not spoken to Mueller about the substance of the investigation since appointing him.
After President Donald Trump's friend, Newsmax CEO Chris Ruddy, said Monday night that Trump is considering firing Mueller, Rosenstein said Mueller can "only be fired for good cause," and it would be his job to put that good cause into writing.
PBS' Judy Woodruff reported
Monday that Ruddy told her after visiting the White House that Trump is "considering perhaps terminating" Mueller -- a decision that would set off a massive political backlash. Ruddy later confirmed the comment to CNN.
Rosenstein also said that because Attorney General Jeff Sessions recused himself from the Russia matter, Mueller could only be fired by Rosenstein himself.
"The chain of command for the special counsel is only directly to the attorney general -- and in this case, the acting attorney general," he said.
Rosenstein also said that having made political contributions "is not a disqualification" from working for the special counsel leading the Russia investigation.
Rosenstein was asked by Sen. Lindsey Graham, R-South Carolina, whether a history of political donations would prohibit someone from being involved in the investigation. "No, senator, it is not a disqualification," Rosenstein said.
Graham then asked whether someone representing Hillary Clinton or the Clinton Foundation would disqualify that person. Rosenstein said that while it depends on the circumstances, "I think the general answer is no."
Three members of the legal team known to have been hired so far by Mueller have given political donations almost exclusively to Democrats, according to a CNN analysis of Federal Election Commission records
Graham disagreed with part of Rosenstein's conclusion.
"I don't think donations are disqualifying at all, but if you represented the Clinton Foundation or Mrs. Clinton herself, that would be a bit disturbing," Graham said.
Members are using the event as a chance to grill Rosenstein about other topics, including the firing of FBI Director James Comey, the investigation into Russian meddling in last year's election and Rosenstein's decision to tap Mueller as special counsel.
Rosenstein said "no, I have not," when asked by Sen. Jeanne Shaheen, a New Hampshire Democrat, whether he has seen good cause to fire Mueller.
"If there were good cause, I would consider it. If there were not good cause, it would not matter to me what anybody said," he said.
Rosenstein's letter critical of Comey's handling of the Hillary Clinton email server investigation served as the Trump White House's first reasoning for firing Comey -- though Trump later undercut that explanation by saying he fired Comey in hopes of ending the Russia probe.
Because Sessions had recused himself from the Russia investigation over his connection to Trump's campaign and his undisclosed meetings with the Russian ambassador, it was Rosenstein's decision to appoint a special counsel to lead the investigation.