Amid a protracted stalemate in Congress over immigration, President Biden has opened a back door to allow hundreds of thousands of new immigrants into the country, significantly expanding the use of humanitarian parole programs for people escaping war and political turmoil around the world.

The measures, introduced over the past year to offer refuge to people fleeing Ukraine, Haiti and Latin America, offer immigrants the opportunity to fly to the United States and quickly secure work authorization, provided they have a private sponsor to take responsibility for them.

As of mid-April, some 300,000 Ukrainians had arrived in the United States under various programs — a number greater than all the people from around the world admitted through the official U.S. refugee program in the last five years.

By the end of 2023, about 360,000 Venezuelans, Cubans, Nicaraguans and Haitians are expected to gain admission through a similar private sponsorship initiative introduced in January to stem unauthorized crossings at the southern border — more people than were issued immigrant visas from these countries in the last 15 years combined.

The Biden administration has also greatly expanded the number of people who are in the United States with what is known as temporary protected status, a program former President Donald J. Trump had sought to terminate. About 670,000 people from 16 countries have had their protections extended or become newly eligible since Mr. Biden took office, according to a new report from the Pew Research Center.

All told, these temporary humanitarian programs could become the largest expansion of legal immigration in decades.

“The longer Congress goes without legislating anything on immigration, the more the executive branch will do what it can within its own power based on the president’s principles,” said Theresa Cardinal Brown, senior adviser at the Bipartisan Policy Center in Washington.

The main challenge, she noted, is that “the courts can come in and say it’s outside the president’s authority, or an abuse of discretion, and take it all away.”

Already, critics have complained that the administration is using unfettered discretionary power that runs afoul of the laws Congress passed to regulate legal immigration, a system based primarily on family ties and, to a lesser extent, employment.

With Mr. Biden expected to kick off his re-election campaign this week, Republicans are likely to focus on what they call his overly permissive immigration policies.

Twenty Republican-led states, including Texas, Florida, Tennessee and Arkansas, have sued in federal court to suspend the parole program for residents of Cuba, Haiti, Nicaragua and Venezuela, arguing that it will admit 360,000 new immigrants a year from those countries and burden states with additional costs for health care, education and law enforcement.

Alabama, one of the plaintiffs, cited estimates that even before these programs, up to 73,000 undocumented immigrants were already living in that state, about 68 percent of them with no medical insurance and 34 percent with incomes below the poverty line, an influx the state said was costing taxpayers about $324.9 million a year.

“This constitutes yet another episode in which the administration has abused its executive authority in furtherance of its apparent objective for immigration policy: open borders and amnesty for all,” Ken Paxton, the Texas attorney general who is leading the states’ lawsuit, said when it was filed.

In adopting the programs for Latin Americans, the Biden administration was responding to widespread criticism over the chaotic situation on the southern border, which last year saw 1.5 million unauthorized crossings. It bypassed years of failed attempts in Congress to legalize undocumented workers already in the country or to make more visas available to employers who wish to bring in temporary workers.

The new parole programs are temporary — most expire after two years, unless they are renewed — but they already are changing the nature of immigrant arrivals. The migrants who were admitted to the country after flooding the border from many of the same conflict-ridden countries last year have not been allowed to work for at least six months, after opening an asylum case.

As a result, many have wound up in shelters in cities like New York, which has struggled to accommodate them.

The humanitarian parole program, in contrast, requires immigrants to first have a sponsor in the United States who will take financial responsibility for settling them in, and expeditiously offers a work permit for those approved. Employers with worker shortages are welcoming the arrivals as an important new labor pool.

The administration’s goal was to discourage the hundreds of thousands of migrants who were arriving at the border by allowing people to apply in a more orderly fashion from their home countries. After the programs began, overall Border Patrol apprehensions at the border reached their lowest levels in two years, led by a precipitous decline in Cubans, Haitians, Nicaraguans and Venezuelans. Average weekly apprehensions declined to 46 in late February from 1,231 in early January, when some of the parole measures were announced.

“The successful use of these parole processes and the significant decrease in illegal crossing attempts demonstrate clearly that noncitizens prefer to utilize a safe, lawful and orderly pathway to the United States if one is available, rather than putting their lives and livelihoods in the hands of ruthless smugglers,” the Department of Homeland Security said in a statement.

Overall border crossings from all nationalities, however, remain near historic highs, even with the new programs.

The programs have divided leaders of Republican states. Some, including those suing, contend that with the new programs, Mr. Biden has effectively kept the country’s doors wide open, although instead of masses of people crossing without authorization, he has invited them in legally.

But the programs have attracted broad support in the business community in some conservative states, like North Dakota, where there is deep concern over worker shortages.

A report last week from FWD.us, a bipartisan pro-immigration group, estimated that about 450,000 immigrants who entered the United States on parole programs from Afghanistan, Ukraine and Latin American countries were filling jobs in industries facing critical labor shortages, including construction, food services, health care and manufacturing.

In North Dakota, where the oil industry has been struggling to hire roustabouts to operate rigs in the region’s notoriously punishing weather, the state Petroleum Council is recruiting people across the western prairie to act as sponsors for new Ukrainian immigrants who can be put to work.

The first 25 Ukrainian families are expected to arrive by July, with hopes that hundreds more will follow soon after.

“The Ukrainians need us, and we need them,” said Ron Ness, president of the council. “We have been working seriously to develop a very big project on a very large scale to attract them.”

In Utah, already home to a thriving Venezuelan community but where unemployment is 2.4 percent, Gov. Spencer Cox has called for states to be allowed to sponsor immigrants to meet their work force needs. Derek Miller, president of the Salt Lake Chamber, said that Utah was “very supportive” of the parole program given the inability of Congress to open new pathways for legal immigration.

“We have 100,000 jobs going unfilled,” Mr. Miller said. “We embrace a process for those who want to contribute to be able to come.”

Employers in Illinois are also gearing up for new arrivals. “This is a breath of fresh air, when we are seeing such a labor shortage,” said Sam Toia, president of the Illinois Restaurant Association in Chicago, who said businesses there were attracting many Ukrainians on parole because of the state’s historical ties to Ukraine.

Many of the new immigrants already have found work. Anastasiia Derezenko of Ukraine crossed the southern border with her husband and two children last year, and the family received the temporary protected status Mr. Biden approved for Ukrainians. She found a job as a certified nurse assistant in Washington State.

“We have decided we don’t want to go back; we want to build our life here,” she said.

Humanitarian parole has been used in the past. The authority granted by Congress to the executive branch in 1952 in fact has evolved into a key tool for expeditiously admitting people who do not qualify under established immigration categories, though rarely to the degree seen lately under the Biden administration.

President Eisenhower used parole authority to allow 15,000 refugees to enter the United States after the Hungarian revolution in 1956. Before the enactment of the Refugee Act of 1980, parole was used to swiftly admit 690,000 Cubans and 360,000 refugees from Southeast Asia after the fall of Saigon.

Over the last several administrations, some of the most consequential immigration policies have resulted from presidents exercising discretion, including former President Barack Obama’s executive action to create the Deferred Action for Childhood Arrivals program, or DACA, which gave young undocumented immigrants work permits and a reprieve from deportation. Mr. Trump used his authority to ban travel into the United States from a list of targeted countries.

But following the earlier moves to parole Cubans and Southeast Asians, Congress quickly granted the ability for them to obtain permanent U.S. residency.

The Biden administration paroled into the United States some 75,000 Afghans evacuees amid the hectic U.S. military withdrawal, but a divided Congress does not appear likely to pass the Afghan Adjustment Act, a bill that would put them on the path to green cards. If it fails to pass, the administration would have to extend their temporary status before it expires in August.

“The challenge today is, we are much less likely to get legislation from Congress that regularizes people who have come,” said Adam Cox, an expert on immigration and constitutional law at New York University.

Muzaffar Chishti, senior fellow at the Migration Policy Institute, cautioned that unless the parolees applied for asylum, or their parole was extended when it expires after two years, many recipients could join the mass of 10.6 million undocumented people already in the country

The United States historically has extended humanitarian exemptions repeatedly, enabling many participants to remain in the United States for decades. Nicaraguans, whose nation was battered by a hurricane, for example, have been allowed to stay since 1998.

The Ukrainian immigrants in western North Dakota are joining a community of Ukrainians that sprang up there in the late 1800s. State officials said that welcoming the newcomers would both achieve a humanitarian goal and help address a shortfall of about 10,000 workers in the oil industry.

Glenn Baranko, who owns a large company that builds pads for drilling rigs and is the great-grandson of Ukrainian settlers, said that his family and friends have already agreed to sponsor 10 people he plans to employ.

“I want them here, and I will help them get their first apartment and make sure their fridge is full until the paychecks start to come in,” he said.

Brent Sanford, a former lieutenant governor who is leading the state’s project to tap into the humanitarian parole program, said the state’s oil industry was keen to sponsor people from additional countries, such as Venezuela, which has a robust petroleum sector, and whose nationals are also eligible for humanitarian parole.

“We are hearing some who come might want to continue and stay in the United States, which is great,” he said.