Stanley Fischer, the vice chairman of the Federal Reserve, said Wednesday that he would resign in mid-October, an unexpected decision that gives President Trump greater leverage over central bank policy.

Mr. Fischer, 73, cited “personal reasons” in a brief letter addressed to Mr. Trump. His four-year term was to have ended next June.

The resignation puts immediate pressure on the Trump administration to replenish the Fed’s depleted board. Mr. Fischer’s departure would leave only three people in the seven board seats, the smallest number of governors in the Fed’s history.

It also means that Mr. Trump can appoint a majority of the Fed’s board, bending the direction of its policy. Mr. Trump has repeatedly said that he wants the Fed to loosen some of the regulatory strictures it has imposed in response to the 2008 financial crisis.

Among the decisions the president will have to make is whether to replace Janet L. Yellen as chairwoman or keep her on when her four-year term ends in early February. He faces a choice between a nominee who, like Ms. Yellen, stresses economic growth, or someone more palatable to conservatives who favor greater emphasis on curbing inflation.

Mr. Fischer joined the Fed’s board in May 2014 after a distinguished career as an academic economist and an international policy maker. He sometimes argued that the Fed should be raising interest rates more quickly, sparring with Ms. Yellen. But he provided reliable support for measures strengthening financial regulation.

In recent months he has joined Ms. Yellen in warning against weakening regulations that have been enacted since 2008. In an unusually frank interview with The Financial Times last month, Mr. Fischer described efforts to roll back those regulations as “dangerous and extremely shortsighted.”

Ms. Yellen thanked Mr. Fischer for leading the Fed’s work to increase financial stability.

“Stan’s keen insights, grounded in a lifetime of exemplary scholarship and public service, contributed invaluably to our monetary policy deliberations,” Ms. Yellen said in a statement that the Fed released with Mr. Fischer’s letter.

Mr. Trump has not been in a rush to refill the Fed’s board. There were two vacancies when he took office, and a third seat opened in the spring. So far the White House has put forward only one candidate, Randal K. Quarles, a Utah investor who was nominated in July to join the board as vice chairman for supervision. The Senate Banking Committee was expected to send his nomination to the full Senate in a vote on Thursday.

Administration officials earlier this year settled on Marvin Goodfriend, a Carnegie Mellon economist, for a second seat, but Mr. Trump has not made the nomination.

As for Ms. Yellen’s position, an administration official, speaking on condition of anonymity, said Wednesday that the president was still reviewing candidates. Gary Cohn, the chief White House economic adviser, has been mentioned as a possible nominee. But a person close to the president said Mr. Cohn had fallen out of favor — although not totally out of the running — after expressing distress last month in an interview with The Financial Times over the administration’s response to violent clashes in Charlottesville, Va.

The Fed’s board had at least five members from 1936 until 2009. The head count was reduced to four during brief stretches in 2009, 2010, and 2014. But by far the longest stretch in Fed history with only four board members began in March of this year.

It is the first time that a majority of votes on the Federal Open Market Committee, which makes monetary policy, have been held by the presidents of the Fed’s regional reserve banks — who, unlike most officials with policy authority, are neither directly elected nor confirmed by the Senate. The committee includes the members of the board and the 12 reserve bank presidents, five of whom hold votes at any given time.

Mr. Fischer spent two decades as a professor at the Massachusetts Institute of Technology, where his students included Mario Draghi, now president of the European Central Bank, and Ben S. Bernanke, Ms. Yellen’s predecessor as Fed chief.

Then, in the late 1980s, he embarked on a second career in public service, first as chief economist at the World Bank, then as a senior official at the International Monetary Fund and as governor of the Bank of Israel. By the time he arrived at the Fed, he was widely regarded as leading expert on both the theory and the practice of central banking.

Analysts said Mr. Fischer’s departure was unlikely to shift monetary policy in the near term. The Fed is widely expected to announce after its next meeting in mid-September that it will begin to reduce its holdings of Treasuries and mortgage-backed securities.

The Fed has raised its benchmark interest rate twice this year, to a range between 1 percent and 1.25 percent. Most officials predicted in June that the Fed would raise rates one more time this year, but sluggish inflation could cause the Fed to hesitate.

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