The US government has threatened to ban Harvard University from enrolling foreign students - after the institution said it would not bow to demands from President Donald Trump's administration and was hit with a funding freeze.

The Trump administration on Monday froze $2.2 billion in federal funding for Harvard after the school refused to agree to a list of White House demands.

The Department of Homeland Security Secretary also announced the termination of two grants totaling more than $2.7 million to Harvard.