Harvard University said on Tuesday it will comply with the demands of President Donald Trump's administration to turn over employment forms for thousands of university staff, but for the time being was not sharing records for those employed in roles only available to students.

In an email to university employees sent on Tuesday, Harvard said that earlier this month it received a notice of inspection and a related subpoena from the Department of Homeland Security, seeking to inspect the I-9, or Employment Eligibility Verification, forms and supporting documentation for university employees.

The I-9 forms, from U.S. Citizenship and Immigration Services, are used to verify the identity and employment authorisation of individuals hired for work in the U.S., according to the agency's website.

Harvard said federal regulations entitle the government to access a U.S. employer's paperwork, including information on employment eligibility.

Harvard has been embroiled in a legal fight with the Trump administration to have its billions of dollars of frozen federal funds restored. It sued the Trump administration earlier this year.

The president has threatened universities with federal funding cuts over pro-Palestinian protests against U.S. ally Israel's war in Gaza, climate initiatives, transgender policies and diversity, equity and inclusion programs.

Rights advocates have raised concerns over free speech, due process and academic freedom.

Harvard said that, for now, it was not sharing records with the government for people employed in roles only available to students as it was determining if such a request complied with privacy protection requirements.

The New York Times reported on Monday that Harvard was open to spending up to $500 million to end its dispute with the government. That amount was more than twice what Columbia University agreed to pay last week to resolve federal probes.

The newspaper said negotiators were still discussing the financial details of the Harvard deal and that Harvard opposed allowing an outside monitor to oversee the deal.

On Monday, the government initiated a probe into Duke University and the Duke Law Journal to determine if the journal's selection of its editors gave preferences to candidates from minority communities.

On Tuesday, the government said it notified Duke of a freeze of $109 million in federal funds. Separately it alleged that the University of California, Los Angeles violated federal civil rights law. Both Duke and UCLA had no immediate comment.