Officials estimated that more than 14,000 migrants have converged on Del Rio, Texas.

The migrants are overwhelming the South Texas town of Del Rio and adding even more strain to an immigration system already buckling under record migration, with hundreds of thousands crossing every month and many already waiting years for hearings.

Even as it faces searing criticism from human rights groups and opposition from some Democratic lawmakers, the administration is pushing forward with a strategy meant to relieve the overflow in Del Rio and deter more Haitians from trying to come to the United States.

Sign up for The Morning newsletter from The New York Times

“We have reiterated that our borders are not open, and people should not make the dangerous journey,” said Marsha Espinosa, assistant secretary for public affairs for the Department of Homeland Security.

The Biden administration has three flights planned for Sunday, according to an official who spoke on the condition of anonymity to discuss evolving plans, and starting on Monday, it will run four flights a day. Most of the passengers will be single adults. Under the proposal, issued 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. But many details — 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 country was struck by a devastating earthquake in August. 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 undocumented migrants at the border.

Border crossings have reached their highest level in decades. More than 200,000 people were intercepted by the U.S. Border Patrol last month, bringing the total this fiscal year to more than 1.5 million.

President Biden, who had pledged to adopt a more humanitarian approach to immigration than his predecessor, has been taking tough measures in a bid to stanch the influx. 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,” Ms. Espinosa said. “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.”

But some Republican critics, such as Senator Tom Cotton of Arkansas, have tied the crisis at the border to Mr. Biden’s desire to offer a path to citizenship to many of the 11 million undocumented immigrants living in the United States.

“As tens of thousands of illegal immigrants come across the border, Joe Biden promises them citizenship,” he wrote on Twitter on Friday night. “He’s making this crisis much worse.”

The flights come as the Biden administration is appealing a court ruling this week that halted a Trump-era public health policy that used the coronavirus pandemic to justify turning back unauthorized migrants at the border. Mr. Biden had continued the policy, resisting calls to lift the measure from immigration and human rights advocates who deride it for preventing asylum seekers from requesting protection.

The Department of Homeland Security closed the Del Rio entry port after more than 14,000 Haitians crossed from Mexico and have been camping out under a bridge, awaiting processing by the U.S. Border Patrol. It said it had sent 400 additional agents to the area, and would send more if necessary, to help with the processing. Response teams from the Department of Health and Human Services have been dispatched there to start providing Covid-19 tests, said the official familiar with the plan.

The department 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 people surrounded by mostly ranch land, thorny brush and mesquite trees that is about 150 miles west of San Antonio.

Carrying their meager belongings, the migrants have been traversing the ankle-deep river between Mexico and Texas. Some are seeking work in the United States, and others are fleeing violence or racial discrimination in other countries. Families wait in dense crowds, sleeping on dirt or milling about in the scorching heat in squalid conditions.

A majority of the migrants have arrived after monthslong journeys over land from Brazil and Chile, where many were granted permission to reside and work after an earthquake struck the country in 2010. The economies of those countries have been battered by the pandemic. To help repatriated Haitians who have not lived in the country for years, nonprofit organizations and some American officials will be stationed at the Port-au-Prince airport to receive migrants when they deplane, the official said.

People who have been firmly resettled in another country are not entitled to asylum in the United States, which suggests that many of the Haitians at the border would have a difficult time winning their claims for protection in the United States unless they could prove that they were experiencing violence.

However, advocates accused the United States of violating international law by expelling people without properly screening them to ascertain whether they have a reasonable claim to fear returning home. The Department of Homeland Security did not respond to a question about whether that was the policy. On Saturday, hundreds had claimed fear and were not put in line for deportation, the official said.

“Part of the problem is, there are a lot of Haitians coming with a whole bunch of statuses,” said Yael Schacher, senior U.S. advocate for Refugees International, a nonprofit organization.

Still, she and others sharply criticized the United States for returning people to Haiti, the Western Hemisphere’s poorest country, plunged into crisis this summer by a natural disaster and the killing of its president.

“Haitians are experiencing a crisis after crisis and deserve compassion,” Representative Ilhan Omar, Democrat of Minnesota, said on Twitter on Saturday. “Instead of stepping up deportation, we should be halting it. It’s shameful that from administration to administration our cruel immigration policies remain.”

Recognizing the difficult conditions in Haiti, the Biden administration recently extended temporary relief from deportation to about 150,000 Haitians already living in the United States, granting them temporary protected status. But tens of thousands have tried to cross into the country since then despite not qualifying for the program, which covers those who entered by July 29, before the recent earthquake.

This week, the United States resumed deportation flights to Haiti under the public health order. Immigration and Customs Enforcement repatriated about 90 Haitians on Wednesday.

Among those deported were families with young children, according to the Haitian Bridge Alliance, an advocacy group, which also said that they had been expelled under Title 42. Many Haitian families have claimed fear and are not being deported, the official said.

ICE Air uses chartered aircraft that have the capacity to transport about 135 people. The Defense Department is expected to provide some planes as well to transfer migrants to other border stations to ease overcrowding in Del Rio. ICE has flown migrants from the Laughlin Air Force Base in Del Rio to El Paso, Tucson and San Diego for processing.

In recent months, the administration has stepped up deportation flights to Mexico, Central America and South America. In August, there were 99 likely removal flights compared with 46 in July and 35 in June, according to Tom Cartwright, who tracks ICE Air flights for Witness at the Border, an advocacy group.

Haitians represent a small share of border crossers, or about 4 percent of the migrants encountered by border agents in August, dwarfed by Central Americans and Mexicans.

But their numbers have swelled in recent months. Nearly 28,000 Haitians have been intercepted by the Border Patrol along the United States-Mexico border in the current fiscal year, which ends on Sept. 30, compared with 4,395 in 2020 and 2,046 in 2019.

Despite the public health measure, along some stretches of the border the United States has not been expelling migrant families with young children because Mexico has refused to accept them. And on some days, Mexicans tell border officials that their shelters are at capacity and can take only a certain number of migrants.

“There is just such confusion among migrants and asylum seekers, about what the situation is on the border and how they can best seek protection,” said Robyn Barnard, the senior advocacy counsel for refugee protection at Human Rights First.

Joselyne Simeus, 32, a native Haitian, had lived in Chile for seven years. When she heard that the United States might allow families to enter, she decided to take her chances. On Saturday, Ms. Simeus and her 5-year-old son, Samuel, were among arrivals crammed under the bridge.

On Saturday, she stood in line to board a Greyhound bus in Del Rio, destined to reach family in Florida and lamented that many in her position were being left behind.

“It is really sad, because many people like me will be returned after everything they went through to get here,” Ms. Simeus said. “I am lucky because I have a child. But many people like me fled because we are desperate. There are no opportunities in Haiti. There is nothing to go back to. I came here because I want a better opportunity.”

Eileen Sullivan reported from Washington, and Miriam Jordan from Los Angeles. Edgar Sandoval and James Dobbins contributed reporting from Del Rio, Texas, and Maria Abi-Habib from Ennery, Haiti.