WASHINGTON — The Biden administration announced on Saturday that it would begin swiftly deporting Haitians who have gathered in the thousands at the southern border in the past week after illegally entering the United States.

The move is meant to relieve the overflow at the South Texas border town of Del Rio and deter more Haitians from trying to come to the United States, a strategy that has drawn searing criticism from human rights groups and opposition from some Democratic lawmakers.

The Biden administration has three flights planned for Sunday, and more could be scheduled for the coming days, according to an official who spoke on the condition of anonymity to discuss the evolving plans. The flights will go to Haiti as well as countries in South America where the migrants have been living.

Under the plan, outlined by the Department of Homeland Security, the administration will “accelerate the pace and increase the capacity” of removal flights to Haiti and other destinations in the next 72 hours. Many details of the plan — like the number of people on each flight or how people will be processed before being placed on a flight — were not immediately clear on Saturday.

The administration temporarily paused deportation flights to Haiti after the devastating earthquake in August, which was followed by a powerful tropical storm after weeks of civil unrest. But the sudden surge in migrant crossings over the past week has prompted it to change course.

The chaotic situation, with thousands of Haitians crossing the Rio Grande each day to reach U.S. soil, has posed a new, urgent challenge for the Biden administration, which has been grappling for months with soaring numbers of unauthorized migrants at the border.

President Biden, who had pledged to enact a more humanitarian approach to immigration than his predecessor, has been taking tough measures in a bid to staunch the influx. But the administration said that its plan for handling the large volume of Haitians was consistent with its enforcement policy.

“Individuals and families are subject to border restrictions, including expulsion,” said Marsha Espinosa, assistant secretary for public affairs for the Department of Homeland Security. “Irregular migration poses a significant threat to the health and welfare of border communities and to the lives of migrants themselves and should not be attempted.”

More than 14,000 Haitians, many carrying mattresses, fruit, diapers and blankets, have crossed the ankle-deep river between Mexico and Del Rio and are camping out under a bridge, awaiting processing by the United States Border Patrol. Some are seeking work in the United States, and others are fleeing violence or racial discrimination in other countries.

To alleviate the pressure on resources, the Department of Homeland Security said that it had dispatched 400 agents to the Del Rio area, and that it would send additional staff if necessary.

It said that it was also transferring migrants to other parts of the border that are currently less overwhelmed than Del Rio, a town of about 35,000 residents surrounded by mostly ranch land, thorny brush and mesquite trees that is about 150 miles west of San Antonio.

Many of the migrants have arrived after monthslong journeys over land from Brazil and Chile, where they had been granted permission to reside after an earthquake devastated the country in 2010. The economies of those countries have been battered by the coronavirus pandemic.

Others have headed to the border after traveling directly to Mexico days or months ago from Haiti.

The resumption of return flights to Haiti comes as the Biden administration is appealing a court ruling that halts the Trump-era policy of blocking migrant families from entering the United States, a policy that has long been criticized by immigration and human rights advocates, and even Vice President Kamala Harris when she was a senator.

“This administration has talked a big game about wanting a humane asylum system,” said Lee Gelernt, a lawyer with the American Civil Liberties Union and the lead in the litigation challenging the public health policy known as Title 42. “It is horrific that the administration is sending a blanket message that the border is closed without acknowledging that asylum seekers have no choice but to flee and seek safety.”

Eileen Sullivan reported from Washington, and Miriam Jordan from Los Angeles.