WASHINGTON (Reuters) -President Donald Trump locked horns with Federal Reserve Chair Jerome Powell during a rare presidential visit to the U.S. central bank on Thursday, criticizing the cost of renovating two historical buildings at its headquarters and pressing the case for lower interest rates.

Trump, who called Powell a "numbskull" earlier this week for failing to heed the White House's demand for a large reduction in borrowing costs, wrapped up his visit to the Fed's $2.5 billion building project in Washington by saying he did not intend to fire Powell, as he has frequently suggested he would.

"To do so is a big move and I just don't think it's necessary," Trump told reporters after the visit.

In a post on his Truth Social media site, Trump later said of the renovation, "it is what it is and, hopefully, it will be finished ASAP. The cost overruns are substantial but, on the positive side, our Country is doing very well and can afford just about anything."

The visibly tense interaction at the Fed's massive construction site marked an escalation of White House pressure on the central bank and Trump's efforts to get Powell to "do the right thing" on rates. It happened less than a week before the central bank's 19 policymakers are due to gather for a two-day rate-setting meeting, where they are widely expected to leave their benchmark interest rate in the 4.25%-4.50% range.

The president has repeatedly demanded Powell slash rates by 3 percentage points or more.

"I'd love him to lower interest rates," Trump said as he wrapped up the tour, as Powell stood by, his face expressionless.

Powell typically spends the Thursday afternoon before a rate-setting meeting doing back-to-back calls with Fed bank presidents as part of his preparations for the session.

The encounter between the two men became heated as Trump told reporters the project was now estimated to cost $3.1 billion.

"I am not aware of that," Powell said, shaking his head. Trump handed him a piece of paper, which Powell examined. "You just added in a third building," the Fed chief said, noting that the Martin Building had been completed five years ago.

White House budget director Russell Vought and Trump's deputy chief of staff, James Blair, who have spearheaded criticism of the renovation as overly costly and ostentatious, later told reporters they still have questions about the project. The two men, who joined Trump during the visit, have suggested poor oversight and potential fraud in connection with it. 

Senate Banking Committee Chair Tim Scott, a Republican who sent Powell a letter on Wednesday demanding answers to his own questions about the renovation, also took part in the visit.

Elevated by Trump to the top Fed job in 2018 and then reappointed by former President Joe Biden four years later, Powell last met with the current president in March when Trump summoned him to the White House to press him to lower rates.

The visit on Thursday took place as Trump battles to deflect attention from a political crisis over his administration's refusal to release files related to convicted sex offender Jeffrey Epstein, reversing a campaign promise. Epstein died in 2019.

The Fed, in letters to Vought and lawmakers backed up by documents posted on its website, said the project - the first full rehab of the two buildings since they were built nearly a century ago - ran into unexpected challenges including toxic materials abatement and higher-than-estimated costs for materials and labor.

Speaking outside of the construction site, Trump said there was "no tension" at his meeting with Powell and that they had a productive conversation about rates.

FED INDEPENDENCE

Ahead of Trump's visit, Fed staff escorted a small group of reporters around the two construction sites. They wove around cement mixers and construction machines, and spoke over the sound of drills, banging, and saws. Fed staff pointed out security features, including blast-resistant windows, that they said were a significant driver of costs in addition to tariffs and escalations in material and labor costs.

The project started in mid-2022 and is on track to be completed by 2027, with the move-in planned for March of 2028.

A visit to the roof of the Eccles Building, a point of particular scrutiny by critics like Scott, who has complained about "rooftop garden terraces," revealed an impressive view of the Lincoln Memorial and the National Mall, according to the pool report.

Staff explained that rooftop seating, although inexpensive, had been removed because of the appearance of it being an amenity and was one of only two deviations from the original plan. The other was the scrapping of a couple of planned fountains.

Market reaction to Trump's visit was subdued. The yield on benchmark 10-year Treasury bonds ticked higher after data showed new jobless claims dropped in the most recent week, signaling a stable labor market not in need of support from a Fed rate cut. The S&P 500 equities index closed largely flat on the day.

Trump's criticism of Powell and flirtation with firing him have previously upset financial markets and threatened a key underpinning of the global financial system - that central banks are independent and free from political meddling.

His trip contrasts with a handful of other documented presidential visits to the Fed. Then-President Franklin Delano Roosevelt visited the central bank in 1937 to dedicate the newly-built headquarters, one of the two buildings now being renovated. Most recently, former President George W. Bush went there in 2006 to attend the swearing-in of Ben Bernanke as Fed chief.