The university, like many colleges and charities, is exempt from federal income and property taxes, saving it billions of dollars. President Trump has questioned whether it should enjoy that status.

The directive to the IRS is a significant escalation of President Trump’s feud with Harvard University and other Ivy League institutions and other nonprofit groups his administration views as “woke.”

The IRS is making plans to rescind the tax-exempt status of Harvard University, according to two sources familiar with the matter, which would be an extraordinary step of retaliation as the Trump administration seeks to turn up pressure on the university that has defied its demands to change its hiring and other practices.