More than 1,000 illegal immigrants were apprehended by U.S. Customs and Border Protection agents near the U.S.-Mexico border early Wednesday -- the largest ever group of migrants ever apprehended at a single time, sources told Fox News on Thursday.

The group of 1,036 illegal immigrants found in the El Paso sector included migrants from Guatemala, El Salvador and Honduras, according to sources.

The group was the largest group of migrants ever apprehended at a single time, sources told Fox News. The discovery was made in the El Paso section of the southern border – which provides support for the counties of El Paso and Hudspeth in the state of Texas and the entire state of New Mexico.

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The record apprehension comes as the U.S. Border Patrol said Tuesday it's working to hire additional staff to manage the processing of migrants at the U.S.-Mexico border.

Right now, stations are overwhelmed with the influx of migrant families, as officials say are agents encountering more and larger groups of more than 100 people dropped in extremely remote locations along the Southwest border.

Officials said the aim of beefing up staff is to take the burden off uniformed agents, who can then go back into the field.

Agents said they are spending more than half their time feeding and caring for migrant families. Paperwork processing alone can take three hours per family. There were 58,474 families apprehended last month, according to CBP.

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In March, the agency said that there was an increase of nearly 106 percent over the same period last year.

A top Border Patrol official told lawmakers in April that authorities have apprehended more families illegally crossing the border between October 2018 and February of this year than during all of the 2018 fiscal year (Oct. 1, 2017-Sept. 30, 2018).

"Much media attention has focused on caravans coming across from Central America," Rio Grande Valley Sector Chief Patrol Agent Rodolfo Karisch told the Senate Homeland Security Committee. "But the fact is that RGV is receiving caravan-equivalent numbers every seven days."

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Border Patrol has about 19,500 agents assigned nationwide and has struggled with hiring for many years — the number of agents peaked at 21,444 in fiscal year 2011.

Many positions require living in remote desert towns across the U.S.-Mexico border. Agents must pass a detailed background check and a lie detector test that has been required since 2012 is a major hurdle, with just a 28% pass rate between 2013 and 2016.

On Thursday, President Trump teased he is going to "have a big statement" on border security "soon" after Politico reported he is considering prohibiting people if they have traveled through a country other than their own before coming to the U.S.

"No, I'm not closing the border," he told reporters. "It has to do with the border, it will be my biggest statement so far."

Fox News' Samuel Chamberlain, Adam Shaw, and The Associated Press contributed to this report.