Texas Attorney General Ken Paxton on Tuesday filed the multi-state lawsuit in a federal district court in Victoria.
Under the program, citizens from Cuba, Haiti, Nicaragua and Venezuela can apply for so-called parole if they meet certain conditions. Applicants must have a sponsor in the U.S. and pass vetting and background checks.
The U.S. has said it will allow up to 30,000 individuals per month from those countries to enter the U.S. by air under this process. Those accepted would be allowed to stay for two years and be eligible to work.
"We can provide humanitarian relief consistent with our values, cut out the vicious smuggling organizations, and enforce our laws to enhance the security of our Southwest border by reducing irregular migration," Department of Homeland Security Secretary Alejandro Mayorkas said in early January.
At the same time, Biden Administration officials stressed there would be consequences for migrants from those countries who crossed the border illegally.
"Effective immediately, citizens from Venezuela, Nicaragua, Cuba, and Haiti who attempt to cross our border without authorization will be swiftly expelled to Mexico, which will accept returns of 30,000 individuals per month who failed to use these new pathways, or their home country," Mayorkas said. "At the same time, we will welcome up to 30,000 individuals per month from these four countries to come safely to live and work here for two years."
Paxton says the program is unlawful and would create a de facto pathway for citizenship.
He said in a written statement Tuesday that the program would invite "hundreds of thousands of aliens" into the U.S. every year and "will only make this immigration crisis drastically worse."
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