The chair of the Federal Reserve closed his eyes and shook his head.

He was about to do something that few senior government officials ever do, at least in public: fact-check President Trump in real time.

Jerome H. Powell has been the target of Mr. Trump’s attacks for weeks because of the central bank’s unwillingness to lower interest rates. Mr. Trump has called him a “moron,” a “numbskull,” a “disaster” and more.

On Thursday, as Mr. Powell accompanied the president on a tour of the Federal Reserve’s headquarters, the Fed chair seemed fed up. The president wanted to take him to task over the cost of renovations to the building, but Mr. Powell was having none of it.

“So we’re taking a look, and it looks like it’s about 3.1 billion,” Mr. Trump started in, prompting Mr. Powell to shake his head. “It went up a little bit — or a lot.”

“So, the 2.7 is now 3.1,” Mr. Trump continued, causing Mr. Powell to recoil and look at the president with a puzzled expression.

Seeming to anticipate Mr. Powell’s objection — the chair said he had never heard the figure, and that no such numbers had come from the Federal Reserve — Mr. Trump reached into his jacket pocket for a document detailing the costs, which he said “just came out.”