A divided Supreme Court on Monday allowed construction to continue on President Trump’s luxury White House ballroom, which has been steadily rising to replace the East Wing the president tore down last fall. In a 5-to-4 vote, the court said the preservationists who challenged the construction of the planned 90,000-square-foot ballroom did not have legal grounds known as standing to bring their lawsuit because they were not directly harmed by the project, estimated to cost $400 million. The majority emphasized that its order was not addressing the legality of the project and instead the question of who could sue to try to block it.

But in practical terms, the order was a significant setback to the most serious legal challenge to the project, meaning the president seems likely to be able to complete construction. Halting the project now would probably require a fresh lawsuit from an individual or group with standing, such as Congress, which would be a nonstarter while Republicans control the House and Senate. In an unusual lineup, Chief Justice John G.

Roberts Jr. and the court’s three liberal justices dissented, saying the construction was “likely unlawful.”The White House is “an iconic American building whose symbolism and history are wrapped up in its architecture,” the chief justice wrote in a lengthy dissent that quoted from Winston Churchill and Theodore Roosevelt. “All the more reason to ensure that those responsible follow the rules in deciding what to tear down and what to build up at the People’s House.”Monday’s order reversed lower-court rulings that would have halted aboveground construction because the judges found that the administration had exceeded its authority by moving ahead with major changes to the White House campus without congressional approval. The ballroom project, which includes a secure military bunker underneath, is just one way Mr. Trump has been aggressively remaking Washington during his second term. He has proposed building a 250-foot triumphal arch near Washington’s border with Arlington, Va.

His allies have been pressing to inscribe his name on the John F. Kennedy Center for the Performing Arts even after a judge ordered it removed from the building. But the ballroom has been particularly personal for Mr. Trump, who has for years said that the White House needed a larger space to host special guests without having to erect a tent on the South Lawn.

The order from the Supreme Court was the second time in less than two weeks that the court weighed in on the project. The first time, on Aug. 21, Chief Justice Roberts issued a one-sentence placeholder known as an administrative stay to buy his colleagues additional time to more fully consider the administration’s request to block the lower-court rulings against the president. The chief justice handles emergency requests from the U.S. Court of Appeals for the District of Columbia Circuit and initially acted on his own.

He did not provide any reasoning for the initial order, which also allowed construction to continue. The new order represents the views of the full nine-member court in a more lasting way. In a social media post on Monday afternoon, the president celebrated the decision, which he said cleared the way for the project’s completion in the summer of 2028.“We are living in the Golden Age of America, and this Building will be one of the Greatest ever constructed in Washington, D.

C.,” Mr. Trump wrote. “The magnificent Ballroom and Military Complex will be something that the entire Country is very proud of.”The challenge to the project was brought by the National Trust for Historic Preservation, a nonprofit chartered by Congress to guard public buildings. The trust argued that a longtime member, Alison K. Hoagland, a District of Columbia resident and architectural historian, had been personally and professionally harmed by the destruction of one of the most prominent public buildings in the United States, which she has routinely walked past an...