Homeland Security Secretary Jeh Johnson on Thursday said agents are seeing a renewed surge of people attempting to sneak into the U.S. through the southwestern border over the past few months, with more than 46,000 caught in October alone.

It’s the highest tally since the surge of illegal immigrant children in the summer of 2014.

The numbers were released two days after the presidential election that culminated a campaign in which the porous condition of the southwest border was a heated topic.

Mr. Johnson said he is scrambling resources to try to contain the situation, including putting more illegal immigrants into detention and urging other countries to expedite the process of taking back their citizens.

“Our borders cannot be open to illegal migration. We must, therefore, enforce the immigration laws consistent with our priorities,” Mr. Johnson said in a statement announcing the numbers.

Republicans say the administration invited the surge through its lenient policies.

In a letter last week to Mr. Johnson, the House and Senate chairmen who oversee immigration policy said it appeared that illegal immigrants were trying to get into the U.S. ahead of the presidential election.

“The numbers are staggering,” the Republican lawmakers said.

Jessica Vaughan, policy studies director at the Center for Immigration Studies, said Mr. Johnson is acknowledging the problem only after its exposure by whistleblowers at U.S. Customs and Border Protection. She said the secretary’s declaration that the border isn’t open to illegal immigrants “is thoroughly insincere and meaningless.”

“If he wanted to put a stop to it, he could, but he has made it obvious that the administration is not interested in doing so, only in putting on a show of enforcement,” she said. “His robotic repetition of the administration’s enforcement priorities make it clear that the policy is for only the most egregious ‘worst of the worst’ criminal aliens to be removed, and no effort will be made to prevent other new arrivals from taking their place.”

President-elect Donald Trump ran his campaign on promises of cracking down on illegal immigrants and on beefing up border security. He reiterated that border security pledge on Thursday as he met with congressional leaders on Capitol Hill, saying it was a top priority for his early days in office.

Rosemary Jenks, government relations director at NumbersUSA, which lobbies for stricter immigration controls, said Mr. Trump can end the surge by changing the tone from the top of government.

“There has to be a very clear public statement from the White House, Jan. 20 or Jan. 21, saying from this day forward we intend to secure our borders and enforce our immigration laws,” she said. “I think that alone will make a huge difference at the border. I think the numbers will almost immediately start to slow down.”

She said the message needs to include a warning that the U.S. will no longer allow migrants to show up at the border and demand asylum.

California ports of entry are being overwhelmed by Haitians who fled their country for South America in 2010 and are now making their way to the U.S. to take advantage of lax immigration policies. They pay thousands of dollars to be smuggled to the border, often with the cooperation of Mexican authorities, and then queue up to enter and claim asylum.

Mr. Johnson acknowledged the spike in asylum-seekers but didn’t list any steps he has taken to combat the problem.

He said he has increased detention capacity to hold adult illegal immigrants traveling alone. Authorities are detaining 41,000 people, up from the daily average of the low 30,000s.

But that will not do much to solve the surge of children and families, who make up a large part of the increased flow, and whom the Obama administration has struggled to contain. Under the current interpretation of federal law, the children are quickly processed and sent to live with sponsors in the U.S. — oftentimes parents who are in the country without permission — while they go through a yearslong deportation process.

As for families, during the initial 2014 surge Mr. Johnson boosted bed space and committed to hold families until they could be deported — making it more likely that they would be kicked out. But after an outcry by immigrant rights advocates, the department relented and now tries to process and release families as quickly as possible.

All told, the 46,195 illegal immigrants nabbed at the border in October was the highest number since June 2014, at the peak of the surge of unaccompanied minors.

Border Patrol officials believe that for each illegal immigrant caught, a corresponding number get through. A spike in apprehensions likely means a spike in successful attempts as well.

Mr. Johnson urged parents considering making the perilous journey north with their children to instead apply for one of the special humanitarian programs the administration has created for migrants to enter the U.S. with permission.

The surge has been a political problem for the Obama administration for years.

In 2014, it helped derail chances for an immigration deal in Congress by exposing the continued holes in border security and the chaotic U.S. enforcement policy that takes years to deport determined illegal immigrants.

The number of illegal immigrant minors dipped in 2015 but spiked again in fiscal year 2016. The number of people traveling together as families hit an all-time high in past 12 months.

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