EXCLUSIVE: Migrant children are arriving at the U.S. southern border at rates faster than they can be processed and transferred to sponsor homes, all while the Biden administration has repeatedly denied that there is a "crisis" at the border, a senior Customs and Border Protection official told Fox News. 

"We are taking in more UACs [unaccompanied alien child] than we can process," the CBP official said. "I don't see how we keep this many kids when we can't find sponsors." The official spoke on condition of anonymity out of fear of retaliation. 

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The number of migrant children in federal custody has surged past 4,000 with roughly 94% of beds for migrant children occupied, the source told Fox News. Migrant children are entering federal custody far faster than they are leaving it, creating an unsustainable backlog, the source said.

Customs and Border Protection releases unaccompanied alien child numbers monthly.

In this Friday, Feb. 19, 2021, file photo, asylum seekers receive food as they wait for news of policy changes at the border, in Tijuana, Mexico. (AP Photo/Gregory Bull, File)

In this Friday, Feb. 19, 2021, file photo, asylum seekers receive food as they wait for news of policy changes at the border, in Tijuana, Mexico. (AP Photo/Gregory Bull, File)

"DHS has continued our close coordination with HHS as it increases its capacity to care for unaccompanied minors and place them with sponsors. Our goal is to ensure that CBP has the continued capability to quickly and efficiently transfer unaccompanied minors after they are apprehended to HHS custody, as is required by U.S. law, and as is clearly in the best interest of the children," a CBP spokesman told Fox News in a statement.

The Biden administration has refused to call the perilous border situation a "crisis."

"We certainly also recognize because the president and our administration has made a decision that the way to humanely approach immigration is to allow for unaccompanied children to come and be treated with humanity and be in a safe place while we’re ... trying to get them into homes and sponsors homes that some more may be come to our border," White House press secretary Jen Psaki said last week. 

She continued: "And there have been, of course, a large flow of children across the border, we recognize that -- but we made a policy decision because we felt it was the humane approach."

Psaki spoke a day after Customs and Border Protection announced that the agency encountered 100,441 individuals in February, a 28% increase over January, the agency said. Of those, 19,246 individuals were in family units, 9,457 were unaccompanied children (UACs) and 71,598 were single adults.

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Earlier in March, a senior DHS official confirmed to Fox News that the number of migrant children in custody along the border has tripled in the past two weeks to more than 3,250 and that more than 1,360 had been held for longer than the allowed three days. 

Meanwhile, the Biden administration is refusing to call the situation a "crisis" as they face an "overwhelming" number of migrants at the southern border while scrambling to construct new facilities to hold child migrants.

People surround a car as it arrives carrying food donations at a makeshift camp for migrants seeking asylum in the United States at the border crossing Friday, March 12, 2021, in Tijuana, Mexico. (AP Photo/Gregory Bull)

People surround a car as it arrives carrying food donations at a makeshift camp for migrants seeking asylum in the United States at the border crossing Friday, March 12, 2021, in Tijuana, Mexico. (AP Photo/Gregory Bull)

"I think there is a challenge at the border that we are managing, and we have our resources dedicated to managing it," DHS Secretary Alejandro Mayorkas said earlier in March.

So far in 2021, the numbers have been higher than in 2019, indicating the crisis or "challenge" could be significantly greater this year, and the administration has made moves to indicate it recognizes that. It has opened up migrant centers to deal both with family units and UACs, and has looked at a Virginia military base and other sites to house child migrants.

Mayorkas, who has denied there is a crisis, recently emailed DHS staff urging them to volunteer to help CBP at the border amid what he described as "overwhelming" numbers.

"Today, I activated the Volunteer Force to support Customs and Border Protection (CBP) as they face a surge in migration along the Southwest Border," Mayorkas said in an email to staff, seen by Fox News.

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"You have likely seen the news about the overwhelming numbers of migrants seeking access to this country along the Southwest Border," he said. "President Biden and I are committed to ensuring our Nation has a safe, orderly, and humane immigration system while continuing to balance all of the other critical DHS missions."

This post has been updated with comment from CBP.

Fox News' Adam Shaw, Peter Hasson and Griff Jenkins contributed to this report.