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Texas Gov. Greg Abbott said Thursday that he had rejected a Biden administration proposal for the Federal Emergency Management Agency (FEMA) to partner with Texas to test and potentially quarantine migrant adults and children surging across the border -- amid a controversy over the release of COVID-positive migrants into Texas.

"Instead of doing their job, the Biden Administration suggested it did not have the sufficient resources and, remarkably, asked Texas to assist them in aiding their illegal immigration program. Texas refused," Abbott said in a statement. "We will not aid a program that makes our country a magnet for illegal immigration."

WHITE HOUSE INSISTS COVID-POSITIVE MIGRANTS ARE NOT BEING RELEASED INTO TEXAS, DESPITE ABBOTT CLAIMS

The Washington Post first reported that the administration wants to use FEMA in South Texas to test and quarantine families and adults before they are released into the interior of the United States.

A spokesperson for Abbott told Fox News that the administration had proposed a partnership with Texas for testing, screening and quarantining -- but that Abbott was not interested as it was the role of the federal government to test those coming into the country, and he feared it would make Texas a "magnet" for illegal immigration, as his statement said.

108 ILLEGAL IMMIGRANTS RELEASED BY BORDER PATROL IN TEXAS TEST POSITIVE FOR CORONAVIRUS, OFFICIALS SAY

It comes after Fox News reported Wednesday that 108 migrants in Brownsville, Texas, have tested positive for the coronavirus following their arrival -- some of whom had then taken buses to other states.

"The unconscionable act by the Biden Administration of releasing COVID-positive illegal immigrants in our state puts the lives of Texans and Americans at risk. Border security is strictly a federal responsibility," Abbott said in his statement. "The federal government alone has the responsibility to test, screen and quarantine illegal immigrants crossing our border who may have COVID."

A DHS spokesperson told Fox News on Friday it is working with Texas officials to provide testing, isolation and quarantine for migrants and that the agreement would see all costs covered by DHS.

"We are eager to get the funding into the hands of the local public health officials along the southwest border, which these local public health officials very much want and need," the spokesperson said. "We hope that Governor Abbott will reconsider his decision to reject DHS’s agreement with the Texan local authorities that would enable the very testing of migrant families that Governor Abbott says he wants."

White House press secretary Jen Psaki said earlier Thursday that the Republican governor's claims are inaccurate. 

"We’re about facts around here; that is not factual," Psaki said. 

Describing how migrants are processed amid the coronavirus pandemic, Psaki defended the administration's policies: "When migrants are placed in alternatives to detention, their COVID-19 testing, our policy, is for COVID-19 testing to be done at the state and local level, and with the help of NGOs and local governments," she said.

Psaki added that is "concluded before they are even moved to stay with family members or others they may know while their cases are being adjudicated."

Psaki added that the administration’s guidance to anyone, "regardless of status," testing positive for COVID-19 or experiencing COVID-19 symptoms, is "to social distance, to wear a mask, and to seek medical attention as needed."

"But in general, our approach and our policy is to work with local governments and NGOs to have testing, to ensure these migrants are tested," Psaki continued. "And that can take place, and that steps for isolation, quarantine and medical care can be taken should that be needed."

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The controversy comes after the Biden administration is facing a surge in migrants at the border and has revived the practice of releasing migrants into the interior of the United States -- a process known as "catch-and-release" and one that had been ended by the Trump administration. 

Republicans have been grilling the Biden administration on the crisis at the border, with House Judiciary Republicans on Thursday calling for hearings into the "sharp" increase in unaccompanied children at the border, and what the administration is doing to tackle it.

Fox News' Griff Jenkins and Brooke Singman contributed to this report.