The latest confrontation between Harvard University and the Trump administration began last month with a far-reaching demand for data on international students.

Kristi Noem, the secretary of the Department of Homeland Security, sent a letter to Harvard requesting, among other things, coursework for every international student and information on any student visa holder involved in misconduct or illegal activity.

Harvard rebuffed parts of the request, and the Trump administration retaliated on Thursday. In one of its most aggressive moves so far against the university, the government said Harvard could no longer enroll any international students, who account for about one-fourth of its total enrollment.

It also expanded its request for records to include any videos of international students, on campus or off, involved in protests or illegal or dangerous activity.

The conflict has only further raised the stakes over the future of America’s oldest and most powerful university.

The administration’s attempt to vacuum up vast amounts of private student data opens a new front in Mr. Trump’s crackdown on dissent from his political agenda. The strategy is aimed at realigning a higher education system the president sees as hostile to conservatives by stamping out what it says is antisemitism on campus and the transgender and diversity policies it says are rooted in “woke” ideology.