WASHINGTON, April 29 (Reuters) - Kevin Warsh, U.S. President Donald Trump's pick to lead the Federal Reserve, cleared a key procedural hurdle on Wednesday, opening the way for him to succeed Jerome Powell next month amid the White House's unprecedented efforts to exert control over the world's most powerful central bank.

The Senate Banking Committee voted 13-11 along party lines to advance Warsh's nomination to the full Republican-controlled Senate, which is expected to confirm him in a vote held the week of May 11. Powell's term as U.S. central bank chief ends May 15.

As the vote took place, Powell was leading what is expected to be his last policy-setting meeting as head of the Fed. The policy-setting Federal Open Market Committee is universally expected to leave its benchmark overnight interest rate unchanged in the current 3.50%-3.75% range, given still-elevated inflation and upward pressure on prices from the disruption to global oil supplies due to the Iran war.

President Donald Trump, who picked Powell for the top Fed job in 2018 but soured on him within months for not cutting interest rates, said he believes his new nominee will deliver the reductions in borrowing costs that he wants.

Warsh, a 56-year-old lawyer, financier and former Fed governor, told lawmakers at his confirmation hearing last week that he had not promised Trump that he would cut rates. But he did vow "regime change" to make the central bank more answerable to the administration and Congress on non-monetary policy matters. 

The vote on Wednesday went forward after North Carolina Senator Thom Tillis dropped his opposition in response to the Department of Justice's decision on Friday to end a criminal investigation into Powell that Tillis viewed as a threat to the Fed's political independence.

"I've got confidence that this investigation is over," Tillis said after casting his vote with the Republican majority, adding that while the Department of Justice does plan to appeal a federal judge's decision in the case, prosecutors assured him the intent is not to reopen the investigation but only to settle a legal matter regarding the department's subpoena power.

Republican Senator Tim Scott, who chairs the Senate Banking Committee, called Warsh "battle-tested and ready to serve, and not only serve, but to lead."

The panel's 11 Democrats, who say they doubt Warsh's promise to set policy without regard to Trump's wishes, voted against advancing the nomination. "Members of this committee who vote for Mr. Warsh and help facilitate President Trump's takeover of the central bank will come to regret it," the committee's top Democratic lawmaker, Senator Elizabeth Warren, said before the vote.

UNCLEAR WHETHER POWELL STAYS ON FED BOARD

Republican leaders in the Senate intend to push ahead with consideration of Warsh's nomination on Thursday, a timeline aimed at holding a confirmation vote in the week of May 11, a source familiar with the process said. That timeline would allow Warsh to be sworn in by May 15 when Powell's leadership term ends.

It is still not clear whether Warsh's ascension would mean Powell's exit from the Fed, or whether the current central bank chief would stay on as a member of its Board of Governors - and, if he does so, whether Trump will follow through on his threat to try to fire him. Such a move would surely draw a legal challenge, as did the president's attempt last summer to fire Fed Governor Lisa Cook.

Powell's board seat runs through January 2028.

Fed chiefs almost always step down to make room for their successors, and Powell is a lawyer whose adherence to regularity runs deep. But he took the view that the government's criminal investigation was political intimidation and part of the Trump administration's efforts to influence how the Fed sets interest rates.

Powell said last month that he would not leave the Fed until the criminal probe was concluded with "finality," and he may yet stay on if he feels doing so is best for the central bank and the country.

U.S. Attorney for the District of Columbia Jeanine Pirro said on Friday she would not hesitate to resume her investigation of Powell "should the facts warrant doing so."

"We would not be at all amazed if he decides to leave on May 15," Evercore ISI analysts wrote on Wednesday. "However, our hunch is that Powell does stay, but in the base case only for some months until all the legal loose ends are wrapped up and Fed chair independence is fully reasserted."