WASHINGTON — The Education Department has moved to ease rules on colleges and universities looking to shift their classes onto the internet, as closures of campuses cascaded on Tuesday with the hastening spread of the coronavirus.

With fears growing in higher education, the department has granted what it said was “broad approval” to schools seeking relief from federal standards as they activated “distance learning” programs that still must comply with higher education laws. A guidance document released on Thursday promised colleges and universities flexibility to adjust calendars and course schedules to accommodate students who cannot meet enrollment requirements or complete internships or study abroad programs.