By Ted Hesson and Dave Graham

WASHINGTON/MEXICO CITY, Thurs. Aug 26, 2021 (Reuters) – Democratic lawmakers and immigration advocates pressed President Joe Biden on Wednesday to take new steps to end an immigration policy begun by his predecessor Donald Trump after the top U.S. court ordered that the “remain in Mexico” program be reinstated.

The policy put in place by Trump, a Republican, forced thousands of asylum seekers to stay in Mexico to await U.S. hearings. In one of his first acts as president in January, Biden, a Democrat, ended the policy, formally known as the Migrant Protection Protocols (MPP).

The conservative-majority Supreme Court on Tuesday ordered that Biden must comply with a Texas-based federal judge’s ruling to revive the program, although federal officials retain some discretion on how to do that. Republican-led Texas and Missouri had challenged Biden’s ending of the program, saying his administration failed to follow the correct legal process.

The MPP was a cornerstone of Trump’s hardline immigration policies. Biden promised what he called a more humane approach to immigration.

U.S. Senate Foreign Relations Committee Chairman Robert Menendez, a Democrat, called on Biden’s administration “to curtail and put a lawful end to the implementation of this disgraceful policy.”

Democratic U.S. Representative Lucille Roybal-Allard also urged the administration to roll back what she called “an inhumane policy that forced asylum seekers, including women and children, to wait in dangerous border cities, placing them in greater risk of exploitation by cartels and criminal organizations.”

Marielena Hincapié, executive director of the Los Angeles-based National Immigration Law Center, said the administration should determine how to comply with the court’s order while still trying to end the program.

“We continue to believe that it was unlawful,” Hincapié said. “It caused severe damage and chaos and disorder.”

The administration could potentially take a number of steps to slow-walk implementation of the MPP program, a Democratic congressional aide told Reuters, speaking on condition of anonymity. One option could be to draw out negotiations with Mexico, the aide said.

The U.S. government has already been in touch with Mexico over the Supreme Court decision, Roberto Velasco, a senior official in the Mexican foreign ministry, said on Twitter.

“Mexico isn’t part of the judicial process, which is a unilateral measure by the United States,” Velasco said.

Mexican officials have privately expressed concern that reinstating the policy could strain Mexico’s ability to absorb more migrants.

The U.S. Department of Homeland Security (DHS) said on Tuesday it would challenge the judge’s ruling requiring the government to revive the policy, but comply with it “in good faith” while it remains in effect.

Texas Governor Greg Abbott, a Republican, lauded the Supreme Court’s action.

“President Biden’s partisan reversal of this policy has helped fuel the record surge in illegal migrants and contributed to an environment on the border that is neither safe, orderly nor humane,” Abbott said.

Arrests of migrants caught crossing the U.S. southern border have reached 20-year highs in recent months.

(Reporting by Ted Hesson in Washington and Dave Graham in Mexico City; Editing by Ross Colvin and Will Dunham)