Federal Reserve Chairman Jerome H. Powell said Wednesday that he wouldn’t leave his post if President Trump fired him in a clash over the central bank’s role in spurring the economy.

In a hearing with undertones about the importance of a strong economy to Mr. Trump’s reelection prospects, Mr. Powell was prodded by Democratic House Financial Services Committee Chairwoman Maxine Waters to stand up to Mr. Trump’s calls for interest rate cuts.

“What would you do if the president calls you and said, ‘I’m firing you. Pack up. It’s time to go’?” Ms. Waters asked. “What would you do?”

“Of course, I would not do that,” Mr. Powell replied.

“I can’t hear you,” Ms. Waters said to laughter in the hearing room.

Mr. Powell repeated, “My answer would be no.”

But he signaled that the Fed is likely to cut interest rates when it meets later this month, citing “greater uncertainty” about the global economy in the past two months.

Ms. Waters cited press reports that Mr. Trump has discussed firing the Fed chairman, and urged him to refuse to “submit to these high-pressure tactics.”

“This president has made it clear that he has no understanding or respect for the independence of the Federal Reserve,” she said.

Asked by Ms. Waters whether the president has the authority to fire him, Mr. Powell replied, “I’ve said what I intended to say on the subject. The law gives me a four-year term, and I fully intend to serve that.”

“I hope everybody heard that,” Ms. Waters said.

The president has criticized Mr. Powell and the Fed board for raising interest rates four times last year, and for failing to cut rates so far this year, saying the policies have impeded economic growth.

White House counselor Kellyanne Conway told reporters Tuesday that Mr. Trump believes “he has the power to fire Jay Powell, but he hasn’t done that. He’s not doing that.”

But Mr. Trump lamented last weekend that the Fed “doesn’t have a clue” and is “our most difficult problem.” The president insisted in an interview last month, “I have the right to demote him, I have the right to fire him.”

Mr. Trump announced plans last week to nominate conservative economist Judy Shelton and Fed official Christopher J. Waller to fill two seats on the Fed board. Both support lowering rates.

The stock market responded positively to Mr. Powell’s strong hint of a coming rate-cut at the Fed’s next meeting in late July. The S&P 500 briefly topped 3,000 for the first time in its history before closing at 2,993.07, up about 0.4%. The Dow Jones Industrial Average rose about 76.71 points to close at 26,860.

Mr. Powell said the Fed will “act as appropriate” to preserve nation’s longest economic expansion, bolstered the market’s expectations of a coming rate cut. He said inflation has been running below the Fed’s objective of 2%, while trade tensions and concerns about global growth “have been weighing on economic activity and the outlook.”

“Overall growth in the second quarter appears to have moderated,” Mr. Powell said. “Many [Fed Open Market Committee] participants saw that the case for a somewhat more accommodative monetary policy had strengthened. Since then, based on incoming data and other developments, it appears that uncertainties around trade tensions and concerns about the strength of the global economy continue to weigh on the U.S. economic outlook.”

Some Democrats expressed skepticism about Mr. Powell’s claim to being uninfluenced by the president. Rep. Carolyn Maloney, New York Democrat, asked why he seemed to be forecasting a rate cut after employers added 224,000 jobs in June, which she called a sign of a strong economy.

While Mr. Powell agreed that the June jobs report was “great news,” he added that “the bottom line for me is the uncertainties of global growth and trade continue to weigh on the outlook.”

Rep. David Scott, Georgia Democrat, urged Mr. Powell to “have no fear” in carrying out his job.

“Stay strong. Be courageous,” Mr. Scott told him. “It is important for this nation and economy of the world that the Federal Reserve remains strongly independent. We in Congress, both Democrats and Republicans, [have] got your back.”

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