The nexus of illegal immigration into the U.S. has shifted away from the southwest border and into the country’s air and sea ports, where more than 54 million visitors checked in last year — and nearly 630,000 of them didn’t go home, according to new numbers released Monday.

Known as visa overstays, the visitors present a different challenge than the border crossers, and one that Homeland Security officials are still trying to figure out how to handle.

“This report shows that we have a problem with visa overstays in the United States,” a senior administration official said in briefing reporters on the new numbers, vowing to step up enforcement to try to cut down on the violations.

The Trump administration’s report stands in contrast to the Obama administration, which played down the numbers last year when officials released a similar report, focusing on the vast majority of travelers who did comply and leave when they were supposed to.

Indeed, more than 98.5 percent of those admitted through airports and seaports departed before their admissions expired in 2016. But the sheer amount of travel — some 54 million visitors who came through those air and sea ports — means even that small overstay rate works out to nearly 740,000 illegal immigrants.

Some of the overstays were short term, and the foreigners did leave eventually, but the majority were long-term problems.

Nearly 630,000 immigrants were still in the U.S. at the end of 2016, for a persistent overstay rate of 1.25 percent.

Student visas and exchange visitors were the worst violators, with some countries averaging overstay rates above 20 percent.

Libya, a country of special interest because of terrorism concerns, saw 43 percent of its students refuse to leave on time, while a staggering 75 percent of students from Eritrea broke the terms of their deal, the report said.

Jessica Vaughan, policy studies director at the Center for Immigration Studies, said those kinds of rates should force a rethink at the State Department, which issues visas, and should spur immigration officials to put more effort into deterring and deporting overstays here in the U.S.

“The fact that more than 700,000 visits were overstayed last year shows just how much we need to step up interior enforcement to create more of a deterrent, not only by identifying and deporting overstays, but by weakening the job magnet by cracking down on employers who hire illegal workers,” she said.

Almost none of the visa overstays are investigated, Homeland Security officials told Congress last year. Just 2,500 visa overstay cases resulted in deportations in 2015, or a fraction of 1 percent of the problem.

While it’s difficult to know exact numbers, some analysts say that for every illegal immigrant nabbed at the border, another one gets through. That means that fewer than 500,000 new illegal immigrants a year have snuck in.

Illegal overstays, meanwhile, easily top that number now, according to the new statistics.

Homeland Security experts say those who come legally then overstay have at least faced some scrutiny, often by State Department employees who issue visas, and then by border officers who make a final determination on everyone admitted.

That’s different than border crossers, who face no inspection whatsoever, and where the identity of those who entered is entirely unknown.

Still, experts point out that at least five of the hijackers in the Sept. 11, 2001, terrorist plot were visa overstays.

The report is years overdue, and the Obama administration struggled to get it done, with then-Homeland Security Secretary Jeh Johnson sending versions back for rewrites.

A partial report was released last year, but it only covered basic tourist and business visas, not student visas or other categories that grant foreigners prolonged access and a chance to make a life in the U.S.

Those additional categories in this year’s report are likely one reason the numbers are higher.

The report only covers arrivals and departures by air and sea, not land ports of entry, where inspection is less thorough — though those crossing are usually locals who are going back and forth regularly, and stay near the border.

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