A leader at the University of Texas said the institution would be eager to work with the Trump administration. Other universities have been more circumspect.

Top academics in the Middle Eastern, South Asian and African Studies Department at Columbia University, including Professors Timothy Mitchell and Gil Hochberg, the department’s chair, say the school is committed to the program’s autonomy.

In some cases, the Trump administration has said existing federal law already gives the president all the power he needs to act.

College administrators throughout the country are closely watching whether Columbia responds to the White House with deference or defiance.