A federal judge on Friday allowed the Biden administration to continue a program that it has used to give temporary legal status to hundreds of thousands of citizens of Cuba, Haiti, Nicaragua and Venezuela.

Known as humanitarian parole, the program has offered people from the troubled countries an alternative to entering the United States illegally, and has been central to the administration’s strategy to curb the influx of migrants arriving at the U.S. southern border.

President Biden has faced considerable criticism for his administration’s handling of the border, and Texas and other Republican-led states had sued the administration to block the parole program. But Judge Drew B. Tipton of the U.S. District Court for the Southern District of Texas sided with the administration, saying the states had failed to establish they had standing on any of their claims.

The Homeland Security secretary, Alejandro N. Mayorkas, said he was pleased by the decision in a statement on Friday, calling the program “a key element of our efforts to address the unprecedented level of migration throughout our hemisphere.”

The ruling is a blow to Texas, which has filed a spate of lawsuits against the Biden administration as part of its effort to shape immigration policy, historically a federal responsibility.

The states that signed onto the lawsuit, including Florida, Tennessee and Arkansas, argued that the program had burdened them with additional costs for health care, education and law enforcement. They also argued that the Biden administration was simply inviting many people who otherwise would have entered the country illegally to come to the United States.