Mr. Trump and Mr. Powell stood awkwardly next to each other in white hard hats discussing the project on Thursday afternoon and debated its overall cost.

The president presented Mr. Powell with a new, higher, cost of the project. “It looks like it’s about 3.1 billion, it went up a little bit or a lot,” Trump said. Mr. Powell closed his eyes and shook his head, explaining that the additional cost was related to the Martin Building, another Fed office that was renovated five years ago.

After Mr. Trump said that the third building is “a building that’s being built,” Mr. Powell corrected him by firing back: “It was built five years ago.”

Following his tour, Mr. Trump called the renovation “a very luxurious situation taking place.” He was particularly critical of the fact that the project included digging beneath the building to create space for parking and additional offices and storage.

Ahead of Mr. Trump’s visit, Fed staff took a small group of reporters and photographers through the site and offered detailed explanations of how contractors needed to deploy seismic protection measures on the upgraded walls and windows with blast resistant glass to ensure that the buildings were secure. They said that creating space beneath the building was not the most expensive part of the project but that it was complicated because the capital was built on swampland. However, the choice was made to move mechanical equipment below ground instead of storing it on the roof.

The structures, which were built in the 1930s, have not been “comprehensively renovated” since then, the Fed has said.

The Fed staff members, who requested anonymity to share details of the project, said that certain amenities that have been cut from the project would not have been especially costly.

Those included the addition of seating on a walkable green roof that was removed from original concept plans over concerns it might appear to be excessive. Fountains and planter boxes that were proposed to sit outside one of the buildings that the Fed took over to expand its footprint were also nixed. Officials said that the fountains were removed from the plan to simplify the project and prevent delays.

The Fed complex, where about 3,000 people work, is scheduled to be completed in 2027. It is a massive construction site, with cranes hovering above and rolls of roofing materials waiting to be affixed. In the board room, where top Fed officials gather to make policy decisions, old murals are covered to protect them from debris.

The two-story board room of the Fed complex, where governors meet to make decisions.Credit…Pool photo by Andrew Harnik

The work is scheduled to be completed by 2027.Credit…Pool photo by Andrew Harnik

White House officials and Republican allies have fixated on certain features that were included in a 2021 plan submitted to the National Capital Planning Commission, a little-known board that has since become pivotal in the administration’s campaign to pressure Mr. Powell to yield to Mr. Trump’s demands to cut interest rates or even resign.

The initial proposal described the inclusion of private elevators and dining rooms for top policymakers, additional water fountains and new marble features. Speaking to lawmakers in June, Mr. Powell denied that those features were part of the latest plan and said media reports of lavish amenities were “misleading and inaccurate.”

In a letter on Wednesday, Senator Tim Scott, a Republican of South Carolina who chairs the Senate Banking Committee, called on Mr. Powell to provide documentation supporting his testimony. The Fed has repeatedly updated its website with information intended to back up Mr. Powell’s statements.

On the tour, Fed staff members explained the inclusion of some new marble on part of the facade. They said it was requested by the National Capital Planning Commission so that it matched marble on the existing building. The rest of an expanded wing, which will provide extra space for offices, will be housed in glass. They also highlighted changes being made to an elevator that services two small conference rooms where meals are sometimes served to officials. Fed staff specified that the rooms were not private and open to other staff. They also made clear that the changes to the elevator would make it compliant with accessibility laws.

As the tour proceeded, it was evident that Fed staff members were anxious about how even small details might be perceived by Mr. Trump.

In the oval entryway of the main Eccles Building, where a security detail and receptionist will screen visitors coming for meetings with Fed governors, the words “Oval Office” were written in marker on a piece of plywood on the wall. The Fed team described the label as a joke but later covered the words with yellow spray paint in an apparent move to avoid angering Mr. Trump.

Staff members at the Fed were anxious about how even small details could be perceived by the president.Credit…Pool photo by Andrew Harnik

The $2.5 billion project, which started in 2022, has ensnared Mr. Powell in controversy.Credit…Pool photo by Andrew Harnik

The cost of the project continues to be the biggest conflict with the White House. The Fed is responsible for keeping inflation low and stable and has for years been trying to wrestle control of price pressures that exploded after the pandemic. The central bank initially misdiagnosed the extent of the inflation problem, making it slow to respond with higher interest rates. They eventually had to raise interest rates in big increments in order to catch up, a process that began in 2022.

Last year, the Fed lowered interest rates by a percentage point as inflation receded and the labor market started to cool off, but since January has held borrowing costs steady because of uncertainty about how Mr. Trump’s policies will affect the economy.

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

Fed staff said the contract with the builders was structured so that the price was not locked in. Instead of using a “firm fixed price” contract, the general contractor, which is a joint venture between Balfour Beatty and Gilbane, was awarded a fee and overhead rate. That means that different parts or packages of the overall project go out for competitive bids and are awarded as the renovation unfolds.

The project has about 80 such packages overall and 20 are left to be bid on, according to Fed staff. They said that tariffs, which Mr. Trump has ratcheted up this year, and rising costs of materials and labor led to the price tag being far higher than what was estimated in 2018 and 2019. The project is about $700 million over budget.

The renovations, which require as many as 800 construction workers over two shifts per day, are expected to be completed in the second half of 2027.

The facade of the Constitution Avenue building.Credit…Pool photo by Andrew Harnik

An excavator working on the ground floor of the Constitution Avenue building on Thursday.Credit…Pool photo by Andrew Harnik

The tour is the latest attempt by the Fed to dispel criticism over the project amid relentless attacks from the Trump administration. The president and top administration officials have sought to undermine Mr. Powell by suggesting he has mismanaged the project. Mr. Trump has also questioned whether “fraud” was committed given the extent of the cost overruns.

The White House’s fixation on the renovations comes as the president has grown increasingly angry over the Fed’s decision this year to keep interest rates steady rather than lower them aggressively as he has demanded. Mr. Trump has called for borrowing costs to be 3 percentage points lower, accusing the Fed of holding back the economy and making payments on the government’s debt much more expensive.

The Fed operates independently of the White House, both in terms of the day-to-day management of the institution as well decisions related to monetary policy. Mr. Trump has sought to erode that independence, calling for more of a say in interest rate decisions as well as direct oversight of the central bank in terms of the rules it imposes on Wall Street, for example.

The renovations mark as escalation in the president’s pressure campaign on the Fed and the attacks have been broadly viewed as a potential avenue for Mr. Trump to try and force Mr. Powell out before his term expires next May. The president can remove a Fed chair only for “cause,” meaning gross misconduct or a violation of the law. He cannot do so because of disagreements over interest rates.

Mr. Trump recently signaled his intention to let Mr. Powell serve out his term, but he has wavered on the issue and just last week showed off a draft letter firing Mr. Powell to House Republicans.

The cost of the project continues to be the biggest conflict with the White House.Credit…Pool photo by Andrew Harnik