If confirmed, Rosenstein will handle the Justice Department's investigation into potential Russian involvement with the 2016 election and the Trump campaign. Attorney General Jeff Sessions recused himself from the probes.
Senators Dianne Feinstein and Al Franken focused on the Russia investigation during Rosenstein's confirmation hearing. They honed in on whether he would appoint a special prosecutor to the case.
"I think the answer is, I'm simply not in a position to answer the question because I don't know the information that they know — the folks who are in that position to make that decision," Rosenstein said at his confirmation hearing Tuesday.
That's not the answer Democrats were looking for.
At least one senator wants to block Rosenstein's nomination unless he commits to appointing a special prosecutor.
But Senate Judiciary Committee Chairman Charles Grassley said it was "premature" to discuss an independent counsel. He voiced his confidence in Rosenstein's judgement.
Rosenstein has spent nearly three decades as a U.S. attorney and served under presidents Bill Clinton, George W. Bush and Barack Obama.
He's litigated a number of high-profile corruption and fraud cases. Most recently, Rosenstein helped indict seven Baltimore police officers on charges of racketeering, corruption and robbery.