The Senate is set to proceed with Kevin Warsh’s nomination to lead the Federal Reserve, after a pivotal Republican lawmaker, Senator Thom Tillis of North Carolina, said on Sunday that he is prepared to lift his blockade and lend his support toward confirmation.

For weeks, Mr. Tillis refused to advance Mr. Warsh or any other nominee to lead the central bank while the Trump administration investigated the current chair, Jerome H. Powell, in an inquiry that many have described as politically motivated.

But Jeanine Pirro, the U.S. attorney for the District of Columbia, said on Friday that the Justice Department would drop the matter. Even though Ms. Pirro said that she would “not hesitate” to reopen the investigation, her move to stand aside proved sufficient for Mr. Tillis, who said on NBC’s “Meet the Press” that he is ready to move forward with a key, first committee vote on Mr. Warsh.

“They have made it very clear that the current investigation is completely and fully ended,” Mr. Tillis said of his conversations with the Justice Department.

Mr. Tillis’s vote is a pivotal one in determining whether Mr. Warsh, who has broad support from Republicans, will be confirmed by the time Mr. Powell’s term officially ends on May 15. Senate Democrats have called Mr. Warsh a “sock puppet,” given Mr. Trump’s insistence that he would only pick someone to replace Mr. Powell who supported lower rates.

Republicans hold a slim 13-to-11 majority on the Banking Committee, which oversees the Fed, meaning Mr. Tillis’s opposition created an insurmountable deadlock there. Lawmakers are set to hold a vote on Wednesday at 10 a.m. to advance Mr. Warsh’s nomination to the full Senate.

If confirmed, Mr. Warsh, will assume leadership of an institution that has had to defend its ability to operate independently amid an extensive pressure campaign from White House for lower interest rates.

The criminal investigation into Mr. Powell and the Fed was just the latest broadside from the administration, coming on the heels of an attempt by Mr. Trump to oust Lisa D. Cook, a sitting governor, last year. That case is currently before the Supreme Court.

Mr. Trump has also threatened to fire Mr. Powell if he decides to stay on at the central bank after his term as chair ends. He can stay on as a governor until 2028.

Mr. Powell has yet to disclose whether he will do so but has stipulated that he will only leave once the investigation into him and the Fed is “well and truly over, with transparency and finality.”

He is likely to face questions about his future this week at a news conference after the Fed’s next policy meeting, at which officials are expected to hold rates steady as they grapple an ongoing energy shock from the war in Iran.