The Biden administration on Thursday said it would expand former President Donald Trump’s wall on the Mexican border and begin deporting thousands of Venezuelans in an effort to cut down on the migrant surge that shows no signs of abating.

The moves are an about-face by the White House, which is under political pressure to stem the flow of people. Criticism is intensifying among Republicans as well as Democratic leaders in New York, Chicago and elsewhere who say the influx is overwhelming their ability to house and feed the migrants.

During his campaign for president, Mr. Biden denounced efforts to build a wall along the U.S.-Mexico border, saying it was “not a serious policy solution.” But on Thursday the administration said it was waiving more than 20 federal laws and regulations to allow for the construction of physical barriers along a portion of the border in South Texas, near McAllen.

In announcing that the U.S. government would begin deporting Venezuelans who enter the United States unlawfully, the Biden administration was reversing a policy of not sending migrants back to the troubled South American country, where years of political unrest and economic turmoil have driven millions of people to flee. Last month alone, 50,000 migrants from that country crossed the southern border, a record number, and they now represent the second largest nationality group, dwarfed only by Mexicans.

The announcement about deportations came only three weeks after the administration granted a temporary legal status to hundreds of thousands of Venezuelan migrants who had already entered the United States unlawfully. That was an effort to make it easier for those migrants to work and, in doing so, reduce the strain on New York and Chicago, which have struggled to serve thousands of migrants, many from Venezuela.

But some experts said that in granting Temporary Protected Status, or T.P.S., to a large number of Venezuelans, the government risked encouraging even more migration from the country, and the deportation announcement on Thursday appeared to be the administration’s answer to those concerns.

On a day when three of Mr. Biden’s cabinet officials were in Mexico to meet with President Andrés Manuel López Obrador, the news about the border wall and deportations underlined the challenges Mr. Biden and his administration were wrestling with, as humanitarian crises around the world drive more migrants to the U.S. border while a deeply divided Congress leaves in place an outdated, dysfunctional immigration system.

In defending the decision to move forward with a segment of the wall, Alejandro N. Mayorkas, secretary of the Department of Homeland Security, said in a statement that the work was a legal requirement stemming from appropriations during the Trump administration. But Mr. Biden still finds himself helping to build a border wall that was one of the signature objectives of his predecessor, even as he maintains that such barriers are ineffective in curbing unlawful entry from Mexico.

In a notice published in the Federal Register on Thursday, Mr. Mayorkas said that easing the laws was necessary to expedite construction of sections of a border wall in South Texas, where thousands of migrants have been crossing the Rio Grande daily to reach U.S. soil.

“There is presently an acute and immediate need to construct physical barriers and roads in the vicinity of the border of the United States in order to prevent unlawful entries into the United States,” Mr. Mayorkas said, adding that waiving laws and other requirements was necessary to complete the work more quickly.

The U.S. Border Patrol in the Rio Grande Valley, where the new stretch of the wall is to be built, had encountered more than 245,000 migrants who had entered the country between ports of entry, or unlawfully, in the 2023 fiscal year that ended Sept. 30, the notice said.

It added that construction would be built with funds appropriated by Congress in 2019 for wall construction in the Rio Grande Valley. That appropriation followed a disaster declaration by the Trump administration amid soaring numbers of border crossers.

Mr. Biden said on Thursday that he had no choice but to use the money for the wall.

“The money was appropriated for the border wall. I tried to get them to reappropriate, to redirect that money. They didn’t. They wouldn’t,” he told reporters, apparently referring to Congress.

Asked whether he thought the border wall was effective, he replied, “no.”

In January 2021, on Mr. Biden’s first day in office, the administration revoked the disaster declaration and halted construction. In a proclamation, he said that, “Building a massive wall that spans the entire southern border is not a serious policy solution.”

Nearly $200 million out of the $1.375 billion that Congress designated for barriers in the Rio Grande Valley was still available, and the money had to be used by the end of the fiscal year that ended Sept. 30, according to the law.

As the number of migrants entering the United States has soared in recent months, Mr. Biden has come under fire from Republican leaders, who have made immigration a core issue in the presidential race, and he has faced increasing pressure from mayors of some Democratic-led cities.

“Given the high flow of people, and the political pressure from the right and left, Biden had to be more assertive on enforcement,” said Muzaffar Chishti, a senior fellow at the Migration Policy Institute, a nonpartisan think tank.

“Even his own party has been asking for strong measures,” he said.

The pace of unlawful entries plummeted in the spring after the end of a pandemic-era measure that allowed the government to swiftly deport migrants. But numbers rebounded over the summer, and on some days have doubled the 4,900 unlawful crossings a day that were recorded in mid-April.

This year, more than 380,000 people bound for the United States have crossed the Darién Gap — a jungle straddling Colombia and Panama — and more were expected to come in October, the most popular month for crossings.

In a bid to stem the tide, the Biden administration over the past year has created new policies to provide legal pathways for Venezuelans, enabling them to apply for legal entry into the country if they have a financial sponsor.

But the program has been oversubscribed, and most Venezuelans do not have connections in the United States.

Venezuelan migration to the United States is a recent phenomenon. Many of the arrivals have no relatives or friends, unlike Mexicans, Haitians and Central Americans who have established networks in the country, to receive them. As a result, many Venezuelans have been sleeping in city shelters and relying on municipal and state governments for other assistance.

While border crossings by Venezuelans contributed to a monthly high in unlawful crossings along the southern border in September, when more than 200,000 people were apprehended, the United States has also experienced a spike of migrants from countries in Africa and Asia, thanks to the global reach of smuggling networks that assure clients entry into the United States.

Mexico has struggled with the tide of people moving through the country. Migrants seeking to elude officials have been riding atop cargo trains to reach the border with the United States, arriving by the thousands each day in cities like Ciudad Juárez and El Paso, across the river in Texas.

At a news conference Thursday morning, the president of Mexico, Mr. López Obrador, said that resumption of wall construction was “contrary” to what President Biden had been arguing.

“I understand there are strong pressures from political groups from the extreme right in the United States,” he said, “especially those who want to take advantage of the migratory phenomenon, the consumption of drugs, for electoral purposes.”

Starr County, Texas, where the 20 miles of wall is to go up, is home to about 66,000 people and is west of the city of McAllen. It is home to the Lower Rio Grande Valley National Wildlife Refuge, which follows the Rio Grande along the river’s last 275-mile stretch. The Clean Air Act and Safe Drinking Water and Endangered Species Act are among the federal laws that the Homeland Security Department will waive to allow construction to proceed.

At least one Democratic lawmaker said he supported the administration’s decision to extend the border wall.

“This is a necessary step to help Texas’ overwhelmed border communities deal with this current surge of migrants,” said Colin Allred, a Democratic congressman who is running for the U.S. Senate against Ted Cruz, the Republican incumbent.

“I have long said that targeted physical barriers have a role to play in securing our border at high traffic areas,” he said, “but this is only a partial solution.”

Comprehensive immigration reform, which only Congress can pass, was vital, he said.

The Biden administration has previously taken small steps to seal portions of high-traffic areas along the border. Last year, it closed gaps in the bollard fence erected by the Trump administration in Yuma, Ariz., which had become a busy crossing point for migrants who surrendered to border agents and claimed asylum.

Mr. Trump erected some 550 miles of the hulking, rust-colored bollard fence along the border, much of it to replace shorter, older barriers. Still, smugglers have successfully loosened beams to dig holes, or have flung rope-ladders over the structure, enabling many migrants to breach the border.

Emiliano Rodríguez Mega in Mexico City and Zach Montague in Washington contributed reporting.