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Homeland Security Secretary Alejandro Mayorkas on Monday admitted to Border Patrol agents that the current rate of release for illegal immigrants apprehended at the southern border is "above 85%," sources told Fox News.

Mayorkas made the remarks when meeting privately with agents in Eagle Pass, Texas, according to three Border Patrol sources who were in the room and heard the remarks themselves.

The conversation happened during the muster for agents in the busy border area. Fox is told Mayorkas was asked directly about comments he made on "Special Report" last week when he was asked by anchor Bret Baier about reporting that over 70% of migrants are released into the U.S. each day.

MAYORKAS ACKNOWLEDGES THAT MAJORITY OF ILLEGAL IMMIGRANTS RELEASED INTO US: ‘I KNOW THE DATA' 

"It would not surprise me at all. I know the data," Mayorkas said. "And I will tell you that when individuals are released, they are released into immigration enforcement proceedings. They are on alternatives to detention. And we have returned or removed a record number of individuals. We are enforcing the laws that Congress has passed. "

Fox is told that on Monday agents pushed him on those remarks, saying that the number is even higher than 70%, and then Mayorkas acknowledged a release rate of "above 85%."

Mayorkas had also said last week on "Special Report" that "well more than a million" migrants are released into the U.S. annually, and argued repeatedly that it is up to Congress to provide more funding and immigration reform to fix what he has called a "broken" system. He said that the agency is limited in detention capacity by funding provided by Congress.

"When somebody enters the country, we place them in immigration enforcement proceedings pursuant to immigration law, and if their claim for relief, their claim to remain in the United States succeeds, then by law they are able to stay here," he said.

The remarks come just two days before the House Homeland Security Committee holds its first impeachment hearing, featuring multiple state attorneys general who will testify about the impact the crisis has had on their states.

The hearing on Wednesday marks the first impeachment hearing after a year of investigations and reports by the House Homeland Security Committee which looked at the handling of the nearly three-year migrant crisis.

Republicans have blamed the historic migrant crisis, which saw 302,000 migrant encounters last month alone on Biden-era policies, including the releases of migrants into the interior -- dubbed "catch-and-release." They have pointed to the broad use of parole, as well as narrowed ICE enforcement and the stopping of wall construction.

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The administration says it is dealing with a hemisphere-wide crisis and needs more funding and comprehensive immigration reform from Congress. It has claimed it is expanding "lawful migration pathways" and increasing consequences for illegal entry, but can only do so much with a "broken" system. Mayorkas and other DHS officials have said that it has removed or returned more than 470,000 people since May, which is more than in the entirety of FY 2019.

At a press availability later on Monday, Mayorkas highlighted the removals and returns, saying it is more than in any other five-month period in the last 10 years.

"In fact, the majority of all Southwest Border migrant encounters throughout this Administration have been removed, returned, or expelled – the majority of them," he said. "We are doing everything we can, within a broken system, to incentivize noncitizens to use lawful pathways, to impose consequences on those who do not, and to reduce irregular migration."

The White House has also requested $14 billion in border funding from Congress as part of its emergency supplemental spending proposal, but that is being held up as Republicans demand significantly more restrictions on the release of migrants into the interior.

Mayorkas said last week that it was that broken system, not administration policy, which was the magnet drawing migrants to the border.

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"What is a magnet is the fact that the time in between an encounter of an individual at the border and their final ruling in their immigration case can sometimes take six or more years. That is a magnet, which is why precisely why I am working with Republicans and Democrats in the United States Senate to deliver a solution for the American people, to deliver a fix to an immigration system that everyone agrees is broken, and that is long overdue," he said.

Separately, the administration last week announced a lawsuit against the state of Texas after Gov. Greg Abbott signed a law that allows state and local law enforcement to arrest illegal immigrants. The lawsuit claims that the law is unconstitutional and interferes with the federal government's authority on immigration matters.

Fox News' Charles Creitz contributed to this report.