Attorneys for Texas are asking a federal appeals court in New Orleans to let the state's law banning "sanctuary cities" take effect.
U.S. District Judge Orlando Garcia blocked much of the law Aug. 31 — the day before it was to take effect.
On Friday, three judges of the 5th U.S. Circuit Court of Appeals will be asked to let the law take effect ahead of a November appeal hearing.
Under the law, Texas police chiefs could face removal from office and criminal charges for not complying with federal immigration officials' requests to detain people jailed on non-immigration offenses.
Various local governments in Texas are fighting the law, which also allows police to inquire about people's immigration status during routine interactions like traffic stops -- a provision Garcia didn't block.
Municipal officials from Dallas, Houston, El Paso, San Antonio and Austin are among the opponents. The American Civil Liberties Union is fighting the law on behalf of the city of El Cenizo. The Mexican American Legal Defense fund represents other localities.
Attorney General Jeff Sessions has praised the Texas law and the Department of Justice filed arguments in support of it, as did several states' attorneys general.
The law's opponents argue in briefs that the law puts law enforcement officers in violation of the Fourth Amendment by requiring them to detain people suspected of illegal immigration without probable cause. They also argue that it illegally puts local police in the federal role of immigration enforcement officers, and that it is unconstitutionally vague as to exactly when a local law enforcement officer would be in violation of the law.
Supporters of the state law say immigration officials have already determined probable cause when they seek to have local officials detain someone. They also argue that federal and local officials have a long history of cooperation on immigration matters and that the law is clear in its prohibition against local government's policies restricting immigration enforcement.
The law, known as Senate Bill 4, would have taken effect Sept. 1 had Garcia not issued a stay last month.
The measure won passage in the Republican-controlled Texas Legislature and was signed by Republican Gov. Greg Abbott despite opposition from business groups, which worried that it could cause a labor-force shortage and send a negative economic message.
Judges James Dennis, Leslie Southwick and Stephen Higginson will hear the arguments. Dennis was nominated to the court by Democratic President Bill Clinton; Higginson, by Democratic President Barack Obama; Southwick, by Republican President George W. Bush.