The Supreme Court sided with the Biden administration on Monday, allowing federal officials to cut or remove parts of a concertina-wire barrier along the Mexican border that Texas erected to keep migrants from crossing into the state.

The ruling, by a 5-to-4 vote, was a victory for the administration in the increasingly bitter dispute between the White House and Gov. Greg Abbott of Texas, an outspoken critic of President Biden’s border policy who has shipped busloads of migrants to northern cities.

Since 2021, Mr. Abbott, a third-term Republican, has mounted a multibillion-dollar campaign to impose stringent measures at the border to deter migrants. Those include erecting concertina wire along the banks of the Rio Grande, installing a barrier of buoys in the river and enacting a sweeping law that allows state and local law enforcement to arrest migrants crossing from Mexico.

In lifting an appeals court ruling that had generally prohibited the administration from removing the wire while the court considers the case, the justices gave no reasons, which is typical when they act on emergency applications. Chief Justice John G. Roberts Jr. and Justice Amy Coney Barrett joined the court’s three liberal members to form a majority.

A spokesman for Mr. Abbott, Andrew Mahaleris, defended Texas’ practices and vowed to keep pressing its case. “The absence of razor wire and other deterrence strategies encourages migrants to make unsafe and illegal crossings between ports of entry,” he said in a statement, adding, “This case is ongoing, and Governor Abbott will continue fighting to defend Texas’ property and its constitutional authority to secure the border.”

Angelo Fernández Hernández, a White House spokesman, embraced the decision and called on Congress to come to a bipartisan deal on changes to the immigration system. “Texas’ political stunts, like placing razor wire near the border, simply make it harder and more dangerous for frontline personnel to do their jobs,” he said in a statement. “Ultimately, we need adequate resources and policy changes to address our broken immigration system.”

A three-judge panel of the U.S. Court of Appeals for the Fifth Circuit last month limited the ability of federal Border Patrol agents to cut the wire. The panel prohibited agents “from damaging, destroying or otherwise interfering with Texas’ c-wire fence” while the appeal is pending, but made an exception for medical emergencies that are likely to result in “serious bodily injury or death.”

Ken Paxton, Texas’ attorney general, sued the administration in October, saying that Border Patrol agents had unlawfully destroyed state property and thwarted the state’s efforts to block migrants from crossing the border. According to the lawsuit, border agents cut the wire at least 20 times “to admit aliens illegally entering Texas.”

Migrants have been injured by the wire, and drownings in the Rio Grande’s swift currents have become more common. In court papers, Mr. Paxton argued that federal officials using bolt cutters and forklifts had destroyed parts of the barrier for no reason other than to allow migrants to enter.

In the Biden administration’s emergency application, Solicitor General Elizabeth B. Prelogar rejected the contention that federal officials had done anything improper. “Border Patrol agents’ exercise of discretion regarding the means of enabling the apprehension, inspection and processing of noncitizens in no way suggests that they cut wire for impermissible purposes,” she wrote.

Calling the appeals court’s injunction “manifestly wrong,” Ms. Prelogar said the barrier interfered with Border Patrol agents’ responsibilities.

“The injunction prohibits agents from passing through or moving physical obstacles erected by the state that prevent access to the very border they are charged with patrolling and the individuals they are charged with apprehending and inspecting,” she wrote. “And it removes a key form of officer discretion to prevent the development of deadly situations, including by mitigating the serious risks of drowning and death from hypothermia or heat exposure.”

The exception for medical emergencies was insufficient, Ms. Prelogar wrote. “It can take 10 to 30 minutes to cut through Texas’ dense layers of razor wire,” she wrote. “By the time a medical emergency is apparent, it may be too late to render lifesaving aid.”

The injunction was also unjustified, Ms. Prelogar wrote. “Balanced against the impairment of federal law enforcement and risk to human life,” she wrote, “the court of appeals cited as Texas’ harm only the price of wire and the cost of closing a gap created by Border Patrol agents.”

Mr. Paxton asked the justices to strike a different balance.

“It is in the public interest to deter unlawful agency action and to respect property rights,” he wrote. “It is also in the public interest to reduce the flow of deadly fentanyl; combat human trafficking; protect Texans from unlawful trespass and violent attacks by criminal cartels; and minimize the risks to people, both U.S. citizens and migrants, of drowning while making perilous journeys to and through illegal points of entry.”

This month, federal officials said that when Border Patrol agents tried to respond to reports of a drowning in an area where the state had placed barriers, they were “physically barred” by state officials. Texas officials disputed that account.

J. David Goodman contributed reporting.

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