The central bank’s leadership consists of 12 regional presidents, who are selected by businesspeople and community leaders from their districts and who share four annually rotating votes on interest rates. The New York Fed president is the most powerful regional leader and has a constant vote on policy.

The rate-setting committee also includes seven governors who are nominated by the president and confirmed by the Senate. Only five of those positions are currently filled, although Mr. Trump has said he intends to nominate another two members to the Fed.

The Fed does not answer to the White House by design: It is removed from politics so that it will make better long-term decisions for the economy, rather than trying to goose the economy going into election years. It is, however, responsible to Congress, which can change the rules that govern it.

That insulation has, historically, helped to fuel criticism that the Fed is removed from the public and in the pocket of bankers. The central bank has long been the target of conspiracy theories, and popular books about it have borne titles like “Secrets of the Temple.”

More recently, the president has placed the central bank firmly in political cross hairs. In a Twitter post last week, he asked whether Mr. Powell or President Xi Jinping of China was a “bigger enemy” of the United States. Mr. Trump has reportedly considered firing or demoting Mr. Powell in the past, and he recently told reporters that he would accept Mr. Powell’s resignation if it were offered.

Despite that pressure campaign, Fed officials have repeatedly pushed back against the idea that they would in any way take the White House’s comments or potential actions into account when setting policy.

“We’re never going to take political considerations into account or discuss them as part of our work,” Mr. Powell said at a news conference in January. “We’re human. We make mistakes. But we’re not going to make mistakes of character or integrity.”