The Trump administration on Friday abruptly moved to restore thousands of international students’ ability to study in the United States legally, but immigration officials insisted they could still try to terminate that legal status despite a wave of legal challenges.

The decision, revealed during a court hearing in Washington, was a dramatic shift by Immigration and Customs Enforcement, even as the administration characterized it as only a temporary reprieve.

The back and forth only contributed to the anxiety and confusion facing international students as the administration has moved to cancel more than 1,500 student visas in recent weeks.