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A Texas mayor is sounding the alarm amid a dramatic spike in migrants crossing the U.S. border, saying his city has reached a "breaking point."

"The city of El Paso only has so many resources and we have come to... a breaking point right now," El Paso Mayor Oscar Leeser, a Democrat, said at a news conference Saturday.

Leeser's comments come as El Paso has faced over 2,000 migrants per day crossing the border and seeking asylum in the city, putting a strain on resources and overflowing the available shelter space.

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El Paso mayor

Mayor Leeser said El Paso has reached its "breaking point" as the border crisis rages. (Fox News)

"So, this is something that we've been prepared for, but these numbers have really escalated a lot quicker than we ever anticipated," he added.

The city is just one of several border cities in Texas and California facing a surge in mostly Venezuelan asylum seekers, according to a Reuters report, with many taking dangerous routes on buses and cargo trains to reach the U.S. border.

Leeser said the city plans to open a new shelter, though on Saturday El Paso chartered five buses to move migrants to cities such as New York, Chicago and Denver. The mayor said the migrants were being moved to the city of their choice, with many lacking transportation to get to their preferred destinations while El Paso's shelter capacity currently can only host 400 people and also has to serve the city's homeless population.

Leeser's office did not immediately respond to a Fox News request for comment.

The El Paso mayor is one of at least two Democratic mayors in Texas over the last few days who have warned about the border crisis affecting their cities.

Eagle Pass Mayor Rolando Salinas told CNN a few days ago that he declared a state of emergency in his city of 30,000 people after 5,000 migrants crossed over the border into the city from Piedras Negras, Mexico. Salinas said Biden has "abandoned" border communities and complained that no one from the White House has reached out amid the crisis.

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Migrants at the border in Texas

Migrants wait to be processed on the Ciudad Juarez side of the border on Sept. 21, 2023, in El Paso, Texas. (Brandon Bell/Getty Images)

"I believe 100 percent [Biden] does, he bears some responsibility for this crisis. I haven't heard from anybody in the administration. The president hasn't put out a statement, the vice president, I haven't heard from anybody," Salinas said.

"We're here abandoned. We're on the border, we're asking for help. This is unacceptable," he stated.

The spike to over 2,000 migrants per day is a dramatic change from just six weeks ago when they were only seeing about 350 to 400 people crossing into El Paso daily. The surge has forced the city to work with the U.S. Border Patrol to find space, with the city and agency teaming up over the last 10 days to provide shelter to about 6,500 people.

Leeser said roughly two-thirds of those arriving in El Paso are single men, while 32% are families and about 2% are unaccompanied children.

Asylum seekers heading to the U.S. travel on a train, in El Carmen

Asylum seekers head to the U.S. on a train after thousands of migrants crossed in recent days, in El Carmen, Mexico, Sept. 21, 2023. (Reuters/Daniel Becerril)

"I think it's really important to note that we have a broken immigration system," Leeser said. "It's the same thing over and over again."

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The U.S. Customs and Border Protection did not immediately respond to a Fox News request for comment.

Reached for comment, a White House spokesperson told Fox News Digital that "President Biden has called on Congress to pass comprehensive immigration reform since his first day in office and House Republicans continue to block it," the spokesperson said.

"Now, House Republicans who claim to care about border security are threatening it by proposing a continuing resolution that would eliminate 800 CBP agents and officers and marching toward a shutdown that would halt pay to tens of thousands of DHS law enforcement personnel."

The spokesperson noted that since President Biden took office, the administration has provided of $1 billion in support for recently arriving migrants and has requested $600 million for the Shelter and Services Program.

"We continue to call on Congress to fulfil that request and provide communities across the country the support they need," the spokesperson said.

Fox News Digital's Chris Pandolfo contributed reporting.