The Supreme Court on Friday revived immigration enforcement guidelines by the Biden administration that had set priorities for deciding which unauthorized immigrants should be arrested and detained, saying the challengers had not suffered the sort of injury that gave them standing to sue.

Justice Brett M. Kavanaugh wrote the majority opinion, joined by Chief Justice John G. Roberts Jr. and the court’s three liberal members, Justices Sonia Sotomayor, Elena Kagan and Ketanji Brown Jackson. Justices Clarence Thomas, Neil M. Gorsuch and Amy Coney Barrett voted with the majority but did not adopt its rationale. Only Justice Samuel A. Alito Jr. dissented.

The guidelines, issued in 2021, focused on “national security, public safety and border security.” But they also gave Immigration and Customs Enforcement agents substantial discretion to decide whether enforcement actions were warranted.

Texas and Louisiana sued to block the guidelines, which they said allowed many immigrants with criminal records to remain free while their cases moved forward, imposing burdens on the states’ justice systems and violating a federal law that they said made detentions mandatory.

Last summer, Judge Drew B. Tipton of the Federal District Court in Victoria, Texas, issued a ruling that blocked the use of the guidelines throughout the nation. A unanimous three-judge panel of the U.S. Court of Appeals for the Fifth Circuit, in New Orleans, refused to pause the ruling.

The Biden administration filed an emergency application asking the Supreme Court to block Judge Tipton’s ruling. In a brief order in July, the court refused by a 5-to-4 vote. But the justices agreed to put the case on a relatively fast track, hearing arguments in November.

They considered three basic issues: whether states had suffered the sort of injuries that gave them standing to sue; whether the guidelines were lawful; and what should happen if the court ruled that they were not. The justices seemed divided on all three questions.

The administration argued that the Department of Homeland Security must be able to set priorities given that the federal government does not have the resources to apprehend and seek to deport all unauthorized immigrants. A law that appeared to make some deportations mandatory by using the phrase “shall remove,” the administration said, was unworkable because Congress had not allocated the resources to allow the executive branch to pursue that vast undertaking.

Lawyers for two states responded that the court’s ruling in the case, United States v. Texas, No. 22-58, would affect perhaps 80,000 people. But they conceded that there were not enough beds to detain that many immigrants.

In a separate but nearly identical case brought by three other states — Arizona, Montana and Ohio — a unanimous three-judge panel of the Sixth Circuit, in Cincinnati, refused in July to block the guidelines.

Chief Judge Jeffrey S. Sutton, writing for the panel, said the guidelines were in keeping with the approaches of previous administrations. “Federal law gives the national government considerable authority over immigration policy,” he wrote.