“Massachusetts is home to thousands of international students who should not fear deportation or be forced to put their health and safety at risk in order to advance their education,” Maura Healey, the attorney general, said in a statement.

Bacow, called the administration’s action reckless and said in a statement that it appeared to have been designed to pressure universities to hold in-person classes “without regard to concerns for the health and safety of students, instructors and others.”.

The two universities said that the new directive would prevent many of their 9,000 combined international students — and hundreds of thousands of students at other universities across the country — from staying in the United States.

The American Council on Education, an industry group, said it planned to file a brief in support of the lawsuit, and some 25 higher education associations, including the American Association of Community Colleges, the Association of American Universities and the Association of Land Grant Universities, were expected to join.

“We have heard from many of our members, and they all share the same concerns about the nature of the guidance,” said Pedro Ribeiro, a spokesman for the Association of American Universities, which represents 65 research institutions.

“The effect — and perhaps even the goal — is to create as much chaos for universities and international students as possible,” the universities said in the lawsuit.

International students, many of whom pay full tuition, are a major source of revenue for American universities, and losing them would be a huge blow to the finances of many public and private schools, which are already suffering losses because of the pandemic.

Hurley, chief executive of the Michigan Association of State Universities, which represents the state’s public universities.

The leaders of many universities, including the University of California Los Angeles, Princeton and Cornell, issued statements this week supporting their foreign students and criticizing the administration’s directive.