Mr. Garcia pointed to the president’s plan to hire tens of thousands of border agents, which was announced in February but has yet to come to fruition because Congress still has not provided the funding. The same is true for Mr. Trump’s centerpiece project, the border wall.

“After it became evident that there wasn’t a dramatic change on the part of the administration, then the smugglers started selling their product again and the flow began to resume,” Mr. Garcia said.

In releasing the data, the administration acknowledged that it had lost ground in its effort to stem immigration. But it also seized on the statistics to make the case that Congress should overhaul immigration laws to deter more people from coming.

The Trump administration and Republicans in Congress have been seeking new border security measures in exchange for permitting 800,000 young undocumented immigrants known as Dreamers to remain in the United States. On Tuesday, the president indicated he would even consider allowing millions more unauthorized immigrants to remain in the country, provided Congress took steps to keep new ones from entering.

The numbers of apprehensions are an indication of border activity, but they do not count those who slip through undetected. Though the recent increase makes clear that the flow of migrants has resumed, the numbers have not approached the crisis levels of 2014, when they reached nearly 70,000 in a single month, many of them children traveling alone. Homeland Security officials noted that the 2017 apprehensions still represented a 40 percent decrease from the year before.

“The final border apprehension numbers of 2017, specifically at the southern border, undeniably prove the effectiveness of President Trump’s commitment to securing our borders,” Tyler Houlton, a spokesman for the agency, said in a statement. He also called on Congress to close what he said were “loopholes” that incentivized illegal immigration and were being exploited by migrants. By that, he seemed to reference the asylum system, as well as special protections for children who cross the border without adult supervision.

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Tens of thousands of people apply for asylum annually. The vast majority are denied, and cases can drag on for years, during which time many applicants are released from custody and establish ties to the United States, eventually deciding to stay illegally. Their numbers have contributed to an ever-growing immigration court backlog, with more than 650,000 cases now pending, up from 520,000 in late 2016, according to the Transactional Records Access Clearinghouse, a research group based at Syracuse University.

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Among those stopped at the border in December were 8,000 families and 4,000 so-called unaccompanied minors. Family detention centers are so full that many families are being let go, with the parents fitted with ankle monitors, the kind of “catch and release” practice that the administration has been trying to avoid all along.

Responding to the growing number of people crossing the border, the White House late last year pulled together an interagency task force, which has been meeting to evaluate a suite of new deterrence policies, including separating parents from their children as their cases work through the courts, which immigration advocates have denounced as cruel.

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“The administration is committed to using all legal tools at its disposal to secure our nation’s borders, and as a result we are continuing to review additional policy options,” Mr. Houlton said.

Regardless of American policy, immigrant advocates said that as long as Central America continued to be crippled by crime and poverty, migrants would continue to flow north. Honduras, Guatemala and El Salvador are often ranked among the most dangerous countries in the world because of drug- and gang-related violence, as well as widespread attacks against women.

A recent contested election in Honduras has also spurred many to seek asylum in the United States since November, the advocates said.

“Based on our observations and interviews, it’s clear that nothing has changed in Mexico or Central America; if anything, things are getting worse,” said Camilo Perez-Bustillo, director of advocacy at the Hope Border Institute in South Texas, which has been analyzing the trends in border crossings for a coming report. “There’s no reason to assume that the numbers would diminish as long as the conditions prevail.”

One recent border crosser, an 18-year-old man from the state of Yoro in Honduras who asked not to be identified because he was here illegally, agreed. He entered the United States on New Year’s Day and has been staying at Annunciation House, the shelter in El Paso, since.

He said he trekked by himself across a mountain west of El Paso known as Mount Cristo Rey, without the help of a smuggler. He said that he had known about Mr. Trump’s policies and stance toward illegal immigrants, but that ultimately, he decided to come anyway.

“Because of the laws and Trump saying ‘no more immigrants,’ I was afraid of being caught,” he said.

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“But at the same time I want to help my family overcome,” he added. “My goal was to come here no matter the risks.”

Before he left Honduras, he overheard other people talk about crossing the border. He said he thought the rumors of a crackdown along the border had been overblown.

“On the road they say there’s a lot of immigration agents and they’ll chase you and turn dogs on you, go after you on horseback and in cars,” he said. “But there’s a lot more freedom here.”