During a Tuesday hearing on the fate of two international students facing deportation, an appeals court judge asked a key question of the Trump administration. Does it believe the students’ speech is protected by the Constitution?

A government lawyer, Drew Ensign, declined to discuss the issue. “Your honor, we have not taken a position on that,” he said, adding, “I don’t have the authority to take a position on that.”

Trump officials have said publicly that they are scrutinizing and seeking to remove noncitizen students who have been involved in campus unrest related to the war in Gaza. Lawyers for the students, Rumeysa Ozturk and Mohsen Mahdawi, have said the moves violate the First Amendment.

In avoiding the topic in the courtroom, at the U.S. Court of Appeals for the Second Circuit in Manhattan on Tuesday, Mr. Ensign illustrated one of the government’s key legal strategies as it tries to remove students, and immigrants more broadly, from the country: Move fast, battle hard on technical issues and save the key constitutional questions for later.

The strategy has confounded immigration lawyers and frustrated their advocates. It has also effectively slowed some cases, including that of Ms. Ozturk, who has been in detention in Louisiana for six weeks, where her lawyers say she is facing medical harm because of her untreated asthma.

Ms. Ozturk, a Turkish student seeking her doctorate in child development at Tufts University, co-wrote an opinion piece published in the school’s student newspaper critical of Israel’s conduct of the war in Gaza. She was handcuffed outside her apartment and taken into custody by masked federal agents on March 25.