The Biden administration vowed to continue fighting to end a controversial Trump-era border policy that forces asylum-seekers to wait out their cases in Mexico, after the Supreme Court ruled against its attempt to rescind the program.

“The Department of Homeland Security respectfully disagrees with the district court’s decision and regrets that the Supreme Court declined to issue a stay,” it said in a statement after the Tuesday night ruling. “DHS has appealed the district court’s order and will continue to vigorously challenge it.”

The Supreme Court denied the administration’s request to temporarily block an Aug. 13 order by U.S. District Judge Matthew J. Kacsmaryk of the Northern District of Texas, a Trump appointee, to reinstate the “Remain in Mexico” policy while the government appealed the lower court’s ruling.

Formally known as Migrant Protection protocols, or MPP, the policy required asylum-seekers to remain in Mexico while their claims were adjudicated. The administration formally ended the policy on June 1.

DHS said it would comply with the district court’s order “in good faith” but will continue its appeal at the district court level even as it reinstates the policy. It also said it had started “diplomatic discussions” with Mexico over how to restart the program.

“It’s not a decision on the overall legality of MPP, which is still very much being fought over … but whether or not the administration could get a breather before having to implement the border [policy],” Jennifer Ibañez Whitlock, policy counsel at the American Immigration Lawyers Association, said of the Supreme Court’s ruling.

Roberto Velasco Alvarez, a senior official in the Mexican foreign ministry, confirmed in a tweet that the U.S. government had been in touch over the ruling and that the two nations will “exchange information” to determine what action Mexico will take “based on the respect of sovereignty and human rights.”

Meanwhile, there are other steps the Biden administration can take to challenge MPP, which it moved to unwind as soon as President Joe Biden took office on the grounds that it was dangerous and inhumane, forcing vulnerable asylum-seekers to remain in Mexico for long periods of time.

For example, Ibañez Whitlock said, they could issue guidance to Customs and Border Protection outlining how to apply MPP to new arrivals, with room for exceptions, similar to how unaccompanied children are exempt from expulsion under Title 42, a Trump-era public health directive used to turn back migrants at the southern border.

“I think they’re going to be looking for a way to thread the needle where they do comply with the order in good faith,” she said. “But they will continue to press the case that they were right to terminate MPP.”

Roughly 70,000 migrants were subjected to the program, according to data gathered by the Transactional Records Access Clearinghouse, a Syracuse University research center.

Human rights advocates have slammed the policy for forcing vulnerable migrants to wait in dangerous areas of Mexico, where they had limited access to legal services and other resources.

The Trump administration paused the program in spring 2020 with the onset of the COVID-19 pandemic and border closures, leaving thousands of migrants waiting in Mexico in limbo for indefinitely postponed court dates.

The Supreme Court’s one-page ruling said the Biden administration failed to show that rescinding MPP was not “arbitrary and capricious.” Texas and Missouri, the states that asked Kacsmaryk to reinstate the policy, had alleged that undoing the program would force them to expend more resources to combat human trafficking.

The 6-3 ruling, which split along ideological lines, provides a glimpse into how the conservative-leaning court is poised to tackle immigration policies. It earned immediate outrage from immigrant advocates, as well as fresh suggestions for how the administration can challenge the Texas judge’s order.

“The government must take all steps available to fully end this illegal program, including by re-terminating it with a fuller explanation,” Omar Jadwat, director of the Immigrants’ Rights Project at the American Civil Liberties Union, said in a statement. “What it must not do is use this decision as cover for abandoning its commitment to restore a fair asylum system.”