The Trump administration said on Monday that foreign university students will have to leave the country if their classes are all taught online - clouding the future of tens of thousands of enrollees and potentially straining budgets at schools struggling to reopen during the coronavirus pandemic.

About 1.1 million foreign students attended US higher education institutions in the 2018-19 school year, according to a report issued by the State Department and the Institute of International Education (IIE), and they made up 5.5 percent of the entire US higher education enrollment.

Most US universities have not decided yet whether they will have all...