Some conservatives on the court asked tough questions of the administration and suggested sympathy for lower court opinions that went against President Joe Biden.

Justice Samuel Alito at one point implied that the lower courts were correct to hold that the Trump program could be necessary in order to comply with the immigration law. And Justice Clarence Thomas suggested that the government has limited discretion to parole those who arrive.

But Chief Justice John Roberts expressed sympathy for the government's argument that it wants to end a program that had been put forward by the previous administration. He seemed puzzled as to how to handle the lower court opinions that interpreted immigration law to require the program -- or one like it.

"What are we to do?" he queried.

The court's three liberals, meanwhile, backed the Biden administration and arguing that requiring the program to remain in place would have severe diplomatic consequences. It was unclear by the end of arguments if there were five votes in favor of Biden's position.

Justice Elena Kagan worried about diplomatic concerns if the court required the Biden administration to continue implementing a program so dependent upon the cooperation of Mexico. She said such a decision would put the United States at the "mercy of Mexico" and that it could change its mind at any time to change conditions.

When a lawyer for Texas defending the Trump-era program suggested that diplomatic relations would not be in play, Kagan responded, "What are we supposed to do? Drive truckloads of people into Mexico without negotiating?"

Under the unprecedented program launched in 2019, the Department of Homeland Security sent certain non-Mexican citizens who entered the US back to Mexico -- instead of detaining them or releasing them into the United States -- while their immigration proceedings played out.

Critics call the policy inhumane and say it exposes asylum seekers with credible claims to dangerous and squalid conditions. Migrants subject to the program -- formally known as Migrant Protection Protocols -- have resided in makeshift camps along Mexico's northern border.

Remain in Mexico is separate from the public health authority, known as Title 42, that allows border officials to turn back migrants encountered at the border, therefore barring them from seeking asylum, unlike "remain in Mexico," which still provides migrants that chance. (Title 42 is the subject of separate legal challenges; a federal judge on Monday temporarily blocked ending that authority.)

Tuesday's case and the political fallout over the Biden administration's effort to end Title 42 next month have again put into sharp focus the politically precarious position for the White House and the uphill battles the White House faces in court.

While Biden himself vowed to end the "remain in Mexico" program upon taking office, he has been stymied by federal courts.

The case raises questions not only regarding immigration law, but also a president's control over policy and his diplomatic relationships with neighboring countries.

"An incoming president will not have the authority to implement his own agenda, and millions of asylum seekers will be left vulnerable to exploitation and human trafficking while being denied their due process rights," Loyola Law School professor Sabrina Talukder, who signed a brief in support of the Biden administration, told CNN.

Initially, Biden's Department of Homeland Security issued a memorandum terminating the program last June. But after two states -- Texas and Missouri -- brought a challenge, a district judge vacated the memo and ordered the policy reinstated.

The court said the administration had not adequately explained its decision-making process in its attempt to end the program in violation of the federal Administrative Procedure Act. Going a step further, the court also interpreted immigration law to require the DHS to return certain noncitizens to Mexico when it lacks sufficient funds to detain them on US soil, despite long-standing discretion that allows authorities to decide who to release or detain.

The DHS tried again last fall, issuing a new memo offering a more comprehensive explanation of its decision to terminate the program, but an appeals court ultimately upheld the district court's ruling and refused to even take under consideration the reasoning put forward in the new memo, suggesting that it had come too late.

"The lower courts in this case adopted unprecedented limitations on the ability of federal agencies to change policy and to issue new decisions in response to adverse court rulings," Andrew J. Pincus, a lawyer at Mayer Brown LLP, said in an interview.

"If upheld by the court, they would dramatically restrict agency decision-making across the government," he added.

As of April 17, more than 2,300 migrants have been sent back to Mexico under the "Remain in Mexico" policy since it was renewed late last year, according to the International Organization for Migration.

Interpreting immigration law

The justices focused on different provisions of immigration law. One section reads that the Department of Homeland Security "shall" detain noncitizens pending their immigration proceeding, while another provision provides that the Secretary "may return" certain non citizens.

Solicitor General Elizabeth Prelogar told the justices Tuesday that the lower courts had relied on erroneous interpretations of federal law to compel DHS to maintain a program that the administration has twice tried to end. She said that the Biden administration had the legal authority to end the program and had determined the benefits are "outweighed by its domestic humanitarian and foreign policy costs."

She said the that the Homeland Security secretary "should be allowed to finally put his policy decision into effect" and that the breadth of the lower court opinions suggested something had gone powerfully "awry."

Prelogar said the law offers the government alternative options for processing applicants, noting that some can be admitted "on parole" and others may be placed in an expedited removal process. She noted that in fiscal year 2021, the DHS processed more than 671,000 migrants under traditional immigration protocols, an average of more than 55,000 a month.

She also argued that the lower court opinion would carry "dramatic foreign-relations implications" because it compels the executive branch to send those from third countries into Mexico -- the territory of a foreign sovereign.

Texas Attorney General Ken Paxton, joined by Missouri Attorney General Eric S. Schmitt, urged the Supreme Court to uphold the lower court opinions. He said the Trump administration had launched the program because "tens of thousands of aliens unlawfully enter the Nation's southern border every month."