President Trump on Friday said he would be “taking away” the university’s status, renewing a threat he made last month. It was not immediately clear if the I.R.S. was moving forward with a change.

Harvard University signaled Friday that it would resist President Trump’s renewed threat to revoke the school’s tax-exempt status, a move for which it said there was “no legal basis” as the president escalated his bitter dispute with the nation’s oldest university.

Harvard stopped short of explicitly pledging a legal challenge to a revocation of its tax status, a change that would upend the university’s finances. But a spokesperson for the university said in a statement that there was “no legal basis to rescind Harvard’s tax-exempt status.”

“Such an unprecedented action would endanger our ability to carry out our educational mission,” the statement said. “It would result in diminished financial aid for students, abandonment of critical medical research programs and lost opportunities for innovation. The unlawful use of this instrument more broadly would have grave consequences for the future of higher education in America.”