The US Supreme Court on Monday temporarily blocked a Texas law that would allow state police to arrest and deport migrants who cross illegally into the United States from Mexico.
The law, known as Senate Bill 4 (SB 4), has been tied up in the courts as Democrat Joe Biden's White House wrangles with Republican-run Texas over it.
Now its fate is in the hands of the Supreme Court, which has blocked the law from going into effect until March 13 while it reviews the case.
In the United States, immigration matters including policing are handled by the federal government, not states.
The Texas law would have made illegally crossing the border a state crime, a move the federal Department of Justice has called unconstitutional.
In a tense presidential election year, Republicans blame Biden for the recent record flow of migrants into the United States.
Democrats have tried to pass tough immigration reforms but the legislation, tied to aid for Ukraine, was scuttled by Republicans in Congress.
The White House says the party of Donald Trump, who is seeking to challenge Biden for the White House again in November, is deliberately sabotaging a bipartisan attempt to find a solution.
Greg Abbott, the Republican governor of Texas and a Trump ally, has decried an "invasion" of the southern border.
The Justice Department has also filed a lawsuit seeking the removal of a floating barrier installed by Texas authorities in the Rio Grande river to stop migrants crossing from Mexico.