A record 1.7 million migrants from around the world, many of them fleeing pandemic-ravaged countries, were encountered trying to enter the United States illegally in the last 12 months, capping a year of chaos at the southern border, which has emerged as one of the most formidable challenges for the Biden administration.

It was the highest number of illegal crossings recorded since at least 1960, when the government first began tracking such entries. The number was similarly high for the 2000 fiscal year, when border agents caught 1.6 million people, according to government data.

Single adults represented the largest group of those detained in the fiscal year that ended Sept. 30, at 1.1 million, or 64 percent of all crossers. There were also large numbers of migrant families — more than 479,000, which is about 48,000 fewer than during the last surge in family crossings in 2019.

But the nearly 147,000 children whom agents encountered without parents or guardians was the largest number since 2008, when the government started tallying unaccompanied minors. Finding shelter for these migrant children, until they can be released to relatives or other sponsors in the country, was one of the president’s earliest challenges. As of Friday, nearly 11,000 remained in government custody.

The crossers hailed from around the globe, many of them seeking economic opportunity as the coronavirus pandemic erased hundreds of millions of jobs. Agents caught people from more than 160 countries in Asia, Africa and Latin America, with Mexico accounting for the largest share.

A public health rule, invoked by President Donald J. Trump at the beginning of the pandemic in 2020 to seal the border, has remained in place under the Biden administration. Over the last 12 months, the Border Patrol has carried out more than one million expulsions of migrants back to Mexico or to the migrants’ home countries. Agents used the public health rule to expel migrants they encountered 61 percent of the time and to expel families 26 percent of the time.

President Biden has walked a fine line between trying to control the influx and put in place a more humane approach to border enforcement. Republicans have blamed Mr. Biden’s promises to reverse Trump-era immigration policies for fueling the surge, as word spread that the country’s borders had become easier to breach.

“What we are seeing at the southern border is a crisis,” Mike Pompeo, a former secretary of state under Mr. Trump, said on Twitter Friday afternoon. “If the Biden Administration would’ve kept the policies we had in place, this would have never happened.”

In particular, Republican lawmakers have been sharply critical of the admission of tens of thousands of unaccompanied children, along with many families, who would have been turned back under the Trump administration. The Border Patrol released nearly 250,000 migrants into the country, including some with instructions to appear before an immigration judge for removal proceedings, according to Customs and Border Protection.

Senator Tom Cotton, Republican of Arkansas, called on Friday for the Biden administration to declare a national emergency on the southern border.

The crossings this year followed a relative lull in 2020, when just over 400,000 people were encountered trying to enter the country illegally. The drop was largely attributed to the pandemic’s impact on international travel, which kept migrants leaving far-flung countries from reaching Mexico, their entry point to the United States.

Even as the Biden administration continues to use the Trump-era public health rule to deter migration, people from Mexico and the Northern Triangle countries — El Salvador, Guatemala and Honduras — have crossed without authorization in high numbers for several consecutive months.

In addition to the pandemic, two hurricanes destroyed livelihoods and homes in Guatemala and Honduras, where extortion and violence from gangs have persisted in many communities, further fueling an exodus.

The sustained increase has led to overcrowding, and sometimes chaos, at processing centers along the border, where migrants must be held until the U.S. authorities have conducted background checks and entered every single person into a computer.

More than 655,000 Mexicans were arrested, the most from any one country, according to the latest data, along with a combined total of more than 700,000 from El Salvador, Guatemala and Honduras. Together, migrants from Mexico and Central America represented 78 percent of the total.

Over the past year, there was a significant jump in the number of migrants — mostly families — from Brazil, which has been in the grips of the worst Covid crisis in South America. More migrants also arrived from Venezuela, Nicaragua and India, among many others.

Southern border apprehensions previously reached such high levels in the late 1990s, peaking in 2000, when many migrants who entered the country unlawfully were drawn to jobs in construction, food processing and restaurants.

As in the past year, most of those who entered were single adults from Mexico. Many of them tried more than once to sneak into the country, usually until they succeeded, because they did not face significant legal consequences, said Jessica Bolter, an analyst with the Migration Policy Institute. She added that there were “lots of incentives for migrants to try to cross over and over.”

When the Trump administration first invoked the current public health rule, known as Title 42, officials said it was needed to avoid the spread of the coronavirus in the United States. But it has had the unintended consequence of encouraging hundreds of thousands of desperate people to make repeated attempts to enter the country. Many of those subjected to the rule are expeditiously returned to Mexico, often by bus, only to try again a few days later.

Before the public health rule was put in place at the beginning of the pandemic, migrants caught entering the country without authorization could be criminally prosecuted and detained for months.

In September, about 25 percent of the arrests were of repeat crossers.

The high rate of recidivism suggests the majority of border crossers in recent years have been caught, which was not the case during previous peaks. The number of Border Patrol agents has increased substantially in the last decade, and technology like heat sensors, cameras and drones makes it difficult to evade capture.

“There were not nearly as many agents, they had little technology, and there were a lot of easy places to cross,” said Jeff Passel, a demographer at the nonpartisan Pew Research Center who studies the population of those who enter without authorization. “Data shows the Border Patrol now catch almost everybody who tries to cross illegally.”

When Mr. Biden took office, the administration was aware of an uptick in the number of migrants heading north, but it appeared to be caught flat-footed by the large jump in the numbers that followed and by how long the trend has lasted.

The data released on Friday also shows a sharp increase in the number of Haitian migrants who crossed last month — more than 17,000, or 38 percent of the total number of Haitians who were caught crossing illegally over the past 12 months. The Biden administration’s response to their arrival in high numbers in Del Rio, Texas, has drawn broad criticism and raised concerns about the mistreatment of Black migrants in particular.

Of the Haitians who crossed in September, 36 percent were turned away under the public health rule, including more than 2,500 who had arrived in family units. In all, the Biden administration used the rule to turn away 54 percent of all the migrants caught crossing illegally last month.

To comply with a recent court order, the Biden administration has said it plans next month to resume a Trump-era policy known as “Remain in Mexico,” which mandates that asylum seekers wait in Mexico for their immigration court hearings in the United States, pending agreement from the Mexican government.

The administration early this year had ended that program, which accounts for some of the increase in crossings this year. The program has been criticized for subjecting thousands of migrant families to violence, including kidnappings for ransom, in Mexican border towns controlled by drug cartels.