A divided Supreme Court on Tuesday allowed Texas to begin enforcing a law that gives police broad powers to arrest migrants suspected of crossing the border illegally while a legal battle over the measure plays out.

The conservative majority's order rejects an emergency application from the Biden administration, which says the law is a clear violation of federal authority that would cause chaos in immigration law.

Texas Gov Greg Abbott praised the order — and the law — which allows any police officer in Texas to arrest migrants for illegal entry and authorizes judges to order them to leave the U.S.

The high court didn't address whether the law is constitutional. The measure now goes back to an appellate court and could eventually return to the Supreme Court. In the meantime, it wasn't clear how soon Texas might begin arresting migrants under the law.

It was also unclear where any migrants ordered to leave might go. The law calls for them to be sent to ports of entry along the U.S.-Mexico border, even if they are not Mexican citizens.

But Mexico's government said Tuesday it would not "under any circumstances" accept the return of any migrants to its territory from the state of Texas. Mexico is not required to accept deportations of anyone except Mexican citizens.

It condemned the Texas law being allowed to take effect, saying it would criminalize migrants and lead to the separation of families, discrimination and racial profiling. The government said it would put its position before the appeals court next considering the law.

"Mexico rejects any measure that allows state or local authorities to handle immigration control, detain or return nationals or foreigners to Mexican territory," the Foreign Affairs ministry said in a statement.

The Supreme Court's majority did not write a detailed opinion in the case, as is typical in emergency appeals. But the decision to let the law go into effect drew dissents from liberal justices Ketanji Brown Jackson, Elena Kagan and Sonia Sotomayor.

"The Court gives a green light to a law that will upend the longstanding federal-state balance of power and sow chaos," Sotomayor wrote in a blistering dissent joined by Jackson.

The law, known as Senate Bill 4, is considered by opponents to be the most dramatic attempt by a state to police immigration since an Arizona law more than a decade ago, portions of which were struck down by the Supreme Court. Critics have also said the Texas law could lead to civil rights violations and racial profiling.

White House press secretary Karine Jean-Pierre called the law "harmful and unconstitutional" and said it would burden law enforcement while creating confusion. She called on congressional Republicans to settle the issue with a federal border security bill.

The advocacy group FWD.us said the Supreme Court's decision could encourage other states to pass laws encroaching on federal authority. Andrea Flores, the organization's vice president for Immigration Policy and Campaigns, said the law will "unjustly target Texas families, including American citizens, longtime undocumented residents awaiting federal relief, and recent migrants seeking legal protections."

Texas, for its part, has argued it has a right to take action over what authorities have called an ongoing crisis at the southern border. The Texas Department of Criminal Justice said in a statement it is "prepared to handle any influx in population" associated with the state law.

Texas sheriffs' offices have been preparing for the implementation of Senate Bill 4 since the state's legislative session last year, said Skylor Hearn, executive director of the Sheriffs' Association of Texas

The law allows police in counties bordering Mexico to make arrests if they see someone crossing illegally, he said. It could also be enforced elsewhere in Texas if someone is arrested on suspicion of another violation and a fingerprint taken during jail booking links them to a suspected re-entry violation. It likely would not come into play during a routine traffic stop, he said.

"I don't think you will see anything ultimately different," Hearn said.

Arrests for illegal crossings along the southern border hit record highs in December but fell by half in January, a shift attributed to seasonal declines and heightened enforcement. The federal government has not yet released numbers for February.

Some Texas officials sounded a cautious note.

"A lot of the local police chiefs here, we don't believe it will survive a constitutional challenge. It doesn't look like it's going to, because a Texas peace officer is not trained. We have no training whatsoever to determine whether an individual is here in this country, legally," said Sheriff Eddie Guerra of Hidalgo County. He serves as president of the Southwestern Border Sheriffs' Coalition representing 31 border counties from Texas to California.

Conservative Supreme Court Justice Amy Coney Barrett suggested her vote in favor of Texas stemmed from the technicalities of the appeals process rather than agreement with the state on the substance of the law.

"So far as I know, this Court has never reviewed the decision of a court of appeals to enter — or not enter — an administrative stay. I would not get into the business. When entered, an administrative stay is supposed to be a short-lived prelude to the main event: a ruling on the motion for a stay pending appeal," she wrote in a concurring opinion joined by fellow conservative Justice Brett Kavanaugh.

The 5th U.S. Circuit Court of Appeals is expected to consider a stay pending appeal Wednesday, and hear additional arguments on the law April 3.

The battle over the Texas immigration law is one of multiple legal disputes between Texas officials and the Biden administration over how far the state can go to patrol the Texas-Mexico border and prevent illegal border crossings.

Several Republican governors have backed Gov. Abbott's efforts, saying the federal government is not doing enough to enforce existing immigration laws.

The Supreme Court in 2012 struck down key parts of an Arizona law that would have allowed police to arrest people for federal immigration violations, often referred to by opponents as the "show me your papers" bill. The divided high court found then that the impasse in Washington over immigration reform did not justify state intrusion.

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Associated Press writers Mark Sherman and Rebecca Santana in Washington, Valerie Gonzalez in McAllen, Texas, Acacia Coronado in Austin, Texas, and Chris Sherman in Mexico City contributed to this report.