The U.S. attorney’s office in the District of Columbia has opened a criminal investigation into Jerome H. Powell, the Federal Reserve chair, over the central bank’s renovation of its Washington headquarters and whether Mr. Powell lied to Congress about the scope of the project, according to officials briefed on the situation.

The inquiry, which includes an analysis of Mr. Powell’s public statements and an examination of spending records, was approved in November by Jeanine Pirro, a longtime ally of President Trump who was appointed to run the office last year, the officials said.

The investigation escalates Mr. Trump’s long-running feud with Mr. Powell, whom the president has continually attacked for resisting his demands to slash interest rates significantly. The president has threatened to fire the Fed chair — even though he nominated Mr. Powell for the position in 2017 — and raised the prospect of a lawsuit against him related to the $2.5 billion renovation, citing “incompetence.”

AN ESCALATING FIGHT

Mr. Trump told The New York Times in an interview last week that he had decided on who he wants to replace Mr. Powell as Fed chair. He is expected to soon announce his decision. Kevin A. Hassett, Mr. Trump’s top economic adviser, is a front-runner for the top job. While Mr. Powell’s term as chair ends in May, his term as a governor runs through January 2028. Mr. Powell has not disclosed whether he plans to stay on at the central bank beyond this year.

“This new threat is not about my testimony last June or about the renovation of the Federal Reserve buildings,” he said. “It is not about Congress’s oversight role; the Fed through testimony and other public disclosures made every effort to keep Congress informed about the renovation project. Those are pretexts.”

He warned that the investigation signaled a broader battle over the Fed’s independence. “The threat of criminal charges is a consequence of the Federal Reserve setting interest rates based on our best assessment of what will serve the public, rather than following the preferences of the president,” he added. “This is about whether the Fed will be able to continue to set interest rates based on evidence and economic conditions — or whether instead monetary policy will be directed by political pressure or intimidation.”

A spokesman for Attorney General Pam Bondi did not comment on the investigation but said Ms. Bondi had “instructed her U.S. attorneys to prioritize investing any abuses of taxpayer dollars.”

The U.S. attorney’s investigation into Mr. Powell underscores Mr. Trump’s larger clash with the Fed. Other broadsides have included an effort to oust Lisa D. Cook, a governor at the central bank whom Mr. Trump tried to fire over allegations of mortgage fraud. Presidents are able to remove officials at the Fed only for “cause,” which has typically meant malfeasance or a dereliction of duty. The Supreme Court will hear arguments for Ms. Cook’s case on Jan. 21.

Congress granted the Fed the authority to set interest rates free of meddling from presidents, whose political fortunes are often tethered to how the economy is faring. Rather, lawmakers stipulated that the central bank should pursue low, stable inflation and a healthy labor market.

Mr. Powell said on Sunday that the Justice Department had served the Fed with grand jury subpoenas. Prosecutors in Ms. Pirro’s office have contacted Mr. Powell’s staff multiple times to request documents about the renovation project, according to an official with knowledge of the investigation who discussed an open inquiry on the condition of anonymity.

Indictments against two of Mr. Trump’s top targets, the former F.B.I. director James B. Comey and Letitia James, the New York attorney general, were thrown out in November by a federal judge. An investigation into Senator Adam B. Schiff, Democrat of California, has yet to yield enough evidence to present to a grand jury.

The renovations at the center of the investigation into Mr. Powell broke ground in 2022 and are set to be completed in 2027. They are estimated to be about $700 million over budget. The project involves expanding and modernizing the Marriner S. Eccles Building and another building on Constitution Avenue, which date to the 1930s.

The Fed has said that neither of those buildings has been “comprehensively renovated” since their construction nearly 100 years ago, suggesting they were in need of a significant overhaul. Part of the project includes removing asbestos and lead contamination as well as making the facilities compliant with laws related to accessibility for people with disabilities.

A 2021 version of the Fed’s proposal described private elevators and dining rooms for top policymakers, water fountains and new marble features, in addition to a rooftop terrace for staff. Pressed at a congressional hearing in June, Mr. Powell denied that many of those features were part of the latest proposal.

“There’s no V.I.P. dining room; there’s no new marble,” he said. “We took down the old marble, we’re putting it back up. We’ll have to use new marble where some of the old marble broke. But there’s no special elevators. There’s just old elevators that have been there.”

Mr. Powell added that the project’s plans had “continued to evolve” and that some features that had been initially incorporated were scrapped.

After Mr. Powell’s testimony, the Fed published a “Frequently Asked Questions” post on its website that reaffirmed Mr. Powell’s answers to lawmakers. The central bank continued to share additional details, including a virtual tour as well as photographs and annotations to the 2021 proposal that prompted the criticism.

In explaining the cost overruns, the central bank cited expenses tied to materials, equipment and labor as well as unforeseen circumstances, such as more asbestos than anticipated and soil contamination.