The Trump administration on Friday asked the Supreme Court to bless the construction of President Trump’s White House ballroom to replace the demolished East Wing.

The planned 90,000-square-foot ballroom has been mired in litigation ever since the president tore down the East Wing in October as part of his plan to dramatically remake the White House campus. But the courts have let Mr. Trump build even while questioning the project’s legality, allowing the ballroom to steadily rise in recent months.

The administration’s request for intervention from the nation’s highest court comes after an appeals court said on Aug. 7 that the president had most likely exceeded his authority by moving ahead with the privately financed project without approval from Congress. The case poses a test of the limits of executive authority for a Supreme Court that has embraced some, but not all, of the president’s agenda. It also presents the justices with yet another challenge to one of Mr. Trump’s signature initiatives.

D. John Sauer, the solicitor general, told the justices on Friday that the project was already 65 percent complete and suggested it was too late to stop construction. A 250-person crew has been working 20 hours a day, seven days a week to build a concrete-and-steel superstructure that now stretches five stories deep and 70 feet high, he said.

“Halting the project will stall this vital construction, making this president — the subject of recurrent assassination attempts — much less safe, and risking future presidents’ safety,” he wrote in the Friday filing.

In its 2-to-1 ruling, the U.S. Court of Appeals for the District of Columbia Circuit said the Constitution gives Congress — not the president — the responsibility to decide when proposed changes to the White House may move ahead.

“Congress has not ceded unfettered authority to the executive branch to dramatically redesign, reshape and reconstruct the White House — the People’s House — to fit a particular president’s desires,” the appeals court ruled.

The appeals court had paused its ruling for two weeks to give Mr. Trump time to appeal to the Supreme Court. His petition landed a week later. In the interim, work on the project continued.

Mr. Sauer asked the justices to immediately pause the appeals court ruling, which would halt construction as of Aug. 21. He said the secure ballroom space and an underground military complex were “vitally required for national security.”

Construction of the ballroom, estimated to cost $400 million, is part of Mr. Trump’s second-term effort to reshape Washington in his style. Stopping the project now, Mr. Sauer said Friday, would leave an incomplete structure in place that would be susceptible to “strong winds during extreme weather, and vulnerable to erosion, water, foundation damage” and other setbacks.

The National Trust for Historic Preservation, a nonprofit chartered by Congress to guard America’s historic buildings, sued to try to stop the ballroom’s construction, asserting that the president had resisted oversight in violation of federal law.

Chief Justice John G. Roberts Jr., who handles emergency filings from the District of Columbia Circuit, on Friday asked the trust to respond to the administration’s request by noon on Tuesday.

Mr. Trump has defended the project, insisting that congressional approval is not necessary and that his plans are no different than previous, more modest renovation projects completed at the White House without consultation with lawmakers. He has said the White House is in need of a large event facility; state dinners and other big events have long been held in tents outdoors because of the lack of such a space.

The president’s legal team has shifted its claims about the project since the litigation began, asserting in recent months that its primary purpose is to add a sprawling underground military complex to improve White House security.

In its filing on Friday, the administration’s lawyers said the trust lacks legal grounds or standing to bring the lawsuit because it does not have a “personal or financial stake” in the outcome.

After the appeals court ruling, Mr. Trump said on social media that “this unjust decision must be overturned by the Supreme Court in its entirety.” He emphasized that the project was vital for national security and military operations.

In April, Judge Richard J. Leon of the U.S. District Court for the District of Columbia ruled that the project exceeded the scale of the kind of minor changes presidents have traditionally made to the White House grounds and required approval from Congress. The judge, however, deferred to the president’s claims about the critical need for an upgrade of the military bunker below the White House. His ruling, upheld by the appeals court, would halt construction of the ballroom but allow renovations below ground to continue, including construction of bunkers, bomb shelters, and military and medical infrastructure.

Despite that ruling, Judge Leon permitted construction to continue temporarily both above and below ground while the litigation played out.

The National Capital Planning Commission, which reviews plans for major projects and renovations, voted to approve the project in April. The president had installed allies on the commission before announcing a design for the ballroom.

The project is being funded by private donations. Democrats and public interest groups have raised conflict-of-interest concerns about the financing because many corporate donors engage in business with the federal government.

Mr. Trump has said that the private funds give him the flexibility to pursue the project at no expense to taxpayers, and that he does not need congressional approval for the overhaul of the White House when taxpayer money is not involved.

But in June, the administration transferred roughly $350 million from the Secret Service to cover security upgrades at the White House, which appeared to be destined for the combined East Wing project.

Seven Republican senators joined Democrats in June in voting to block the construction on the project until Congress had formally authorized it, but the measure failed to secure the 60 votes needed to pass.