Donald Trump has accused leading US universities, including Harvard, of breaking federal laws on large foreign donations, escalating his attack on the country’s educational establishment.

The president signed an executive order on Wednesday directing federal agencies to enforce a law on foreign gifts to American universities — although it was not immediately clear how, or if, any school had violated the rule.

“There are currently laws on the books requiring certain disclosures of universities when they accept large foreign gifts. We believe that certain universities, including, for example, Harvard, have routinely violated this law,” White House staff secretary Will Scharf said, speaking at the White House. “This law has not been effectively enforced,” he added.