Gov. Greg Abbott of Texas has instructed state officials to end contracts with the Biden administration for shelters in the state that hold migrant children and teenagers who have been arriving alone, in record numbers, to the southwest border.

The order could affect thousands of migrant children waiting to be united with family members or other sponsors in the United States, and could potentially create a new public relations challenge for President Biden.

“The Biden Administration’s immigration policies are failing Texans, causing a humanitarian crisis in many Texas communities along the border,” Mr. Abbott, a Republican who has been calling for Mr. Biden to crack down on illegal immigration, said in the order, issued Monday.

The directive, which is part of a disaster declaration, applies to agreements between state-licensed shelters for children and the Department of Health and Human Services. There are more than 50 such shelters in Texas.

“If the governor actually implements the order, it could displace more than 4,000 children,” Leecia Welch, a lawyer and the senior director of the legal advocacy and child welfare practice at the National Center for Youth Law, said. “And it would impact many more in the future given that many licensed beds are currently unused. At best, it’s creating a big mess and it could be a total disaster.”

The Department of Health and Human Services said it was reviewing the Texas order and did not plan to close any shelters in the state as a result of it.

The state told the shelters that by the end of August, “you must wind down any operations at your child-care facility that provide care under a federal contract to individuals who are not lawfully present in the United States.”

The order does not cover the emergency shelters that the federal government set up earlier this year to house the surge in migrant children at the border. The situation was one of the Biden administration’s earliest challenges and has become a favorite line of attack from Republicans.

As of Wednesday, there were close to 17,000 migrant children under the care of Health and Human Services, including more than 8,000 living in the agency’s network of shelters across the country that have been licensed for federal use, according to a report obtained by The New York Times. If Texas is successful in ending its contracts, it could lead to thousands of children being transferred to emergency sites that have a lower standard of care.

“This attack is against children,” Representative Veronica Escobar, Democrat of Texas, said on Twitter on Wednesday about Mr. Abbott’s order.

Accepting migrant children who arrive alone on the southern border is one of a spate of immigration policy changes that Mr. Biden made when he came into office. The Trump administration had been using a public health emergency rule to turn away migrant children at the border because of the pandemic. On Tuesday, the Homeland Security Department officially ended another widely criticized Trump-era program that stalled the asylum claims of more than 25,000 migrants, leaving them in administrative limbo in Mexico where they faced threats of violence.