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By Suzanne Gamboa and Julia Ainsley

The Department of Homeland Security began rolling out in El Paso, Texas, Wednesday its policy of requiring asylum seekers to stay in Mexico while they await court hearings in their cases, NBC News has learned.

A DHS official, who spoke on condition of anonymity, said people subject to the the policy, called Migrant Protection Protocols by the Trump administration, will be required to remain in Mexico beginning later this week.

The policy began in January at the San Ysidro Port of Entry in San Diego, where migrants were told to wait in Tijuana, Mexico, while their asylum requests were processed.

The waits are now imposed on migrants trying to cross anywhere in the San Diego sector of the California-Mexico border.

A mother and her son are given arm bands after turning themselves in to U.S. Border Patrol agents to claim asylum after crossing the Rio Grande in El Paso, Texas, on Tuesday.Paul Ratje / AFP - Getty Images

The administration has been trying to slash the number of people who cross the border at ports of entry or who enter the U.S. without legal documentation and request asylum.

Asylum cases can take months or years to complete. Previously, asylum seekers with pending cases were allowed to wait them out in the United States.

The administration has defended the new policy as necessary to protect migrants from danger and end exploitation of immigration laws. It is also designed to curb the number of immigrants the government must keep track of while they await the outcomes of their cases.

But it has led to dangerous conditions for migrants waiting in Tijuana, Mexico, for the chance to formally request asylum because of violence, crowded encampments and vulnerability to local gangs, NBC News reported.

Some are concerned the same situation awaits those wanting to enter El Paso from Ciudad Juarez, Mexico, the city just across the border.

The administration plan drew an angry rebuke from U.S. Rep. Veronica Escobar, D-Texas, who represents El Paso.

"With this shameful policy, the administration is endangering lives, abandoning its obligation to bring forward smart solutions for our broken immigration system, and imposing on another country the task of solving our immigration challenges," Escobar said in a statement.

"Enough is enough. I will soon introduce legislation to ensure no funds are provided for this misguided policy," she said and called on other representatives to "stand up against Trump's anti-immigrant agenda and join me in the effort."

Children who come alone to the border are excluded from the "remain in Mexico" policy, but those traveling with their families are not, meaning they also may be turned back to Mexico while they wait for their immigration court date.

The policy has created obstacles for attorneys trying to represent clients in asylum cases. Lawyers don't know whether they need visas in Mexico, have to try to find their clients who may not be staying at shelters and communication can be a problem. The American Civil Liberties Union is challenging the policy in a lawsuit.

A federal immigration judge hearing asylum cases in San Diego questioned a government attorney on how the government can do the judicial work required for applicants made to wait in Mexico, Reuters reported. Judge Jonathan Simpson asked the attorney how the court would serve notices to migrants in Mexico without home addresses.

"I don't have the answer," government attorney Robert Wetteis responded, according to Reuters.

The expansion comes as El Paso experiences a rise in the number of people stopped for trying to enter the U.S. without proper documentation. The apprehended migrants are processed and eventually released, which recently has inundated Annunciation House, a local non-profit, and its partners, that are scrambling to shelter them.

On Tuesday, so many people were released by government officials, the El Paso city-county Office of Emergency Management readied a local recreation center to house about 150 individuals.

In the end, Annunciation House, which has been sheltering many of the migrants, found them hotel rooms.

But on Wednesday, more migrants were being released. Ruben Garcia, Annunciation House executive and legal director, said Immigration and Customs Enforcement informed him it would be releasing 283 people in the morning and another 282 at noon.

Many of these people, if they are unable to get on a bus departing the day of their release, will stay at Annunciation House until they can, usually not more than two or three days later.

“I’m going to distribute those people among 11 different hospitality sites we have. That’s the way it is every single day,” Garcia said.

Annunciation House operates solely on donations and has spent about $1 million on hotels over time, he said.

The Border Patrol said in a statement Tuesday that it has averaged about 570 apprehensions a day over the last 30 days in its El Paso sector, and that 90 percent of the apprehensions in that period occurred in the El Paso metropolitan area.

The El Paso sector is 125,500 square miles that includes all of New Mexico, and the two westernmost counties in Texas, El Paso and Hudspeth. The sector consists of 268 miles of border.

On Tuesday, Customs and Border Protection said it apprehended two groups of 446 people total in El Paso within a span of five minutes in the early morning.

Agents “encountered” the first group near tall steel fencing along the U.S. side of the border and just west of Bowie High School, which is less than a mile from the Rio Grande international boundary, CBP said. They were discovered at 2:45 a.m.

Then at 2:50 a.m., agents “encountered” a second group of 252 people, who had crossed the border illegally near downtown El Paso, CBP said.

Garcia said he and other advocates don't dispute that El Paso is seeing more immigrants arrive. But he said he takes issue with how they are being characterized — as if all are violent or criminals.

He wants the public polled about the words found at the base of the Statue of Liberty: "Give me your tired, your poor, your huddled masses yearning to breathe free."

"If we no longer want to live up to that," he said, "is it time to take down the Statue of Liberty?"

Suzanne Gamboa reported from Austin, Texas, and Julia Ainsley from Washington, D.C.

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