As the era of Donald Trump's presidency gets under way, university heads need to speak up about wanting international students, according to Brown University President Christina Paxson.

"They are vital for what we do," she told CNBC's "Squawk Box" on Thursday about international students on campus.

Her comments came in response to a Trump order signed earlier this month that restricts immigration from some Muslim-majority nations. Paxson said Brown University had "a couple students who are still not able to get back into Brown to do their education."

Trump's latest immigration order watered down an earlier ban, removing Iraq from the list, and no longer barring any lawful permanent residents from entering. Although the order has been blocked by the courts, it has left disruption and confusion in its wake.

"The president, his policies, are sending out a message to the world that international students may not be welcome in the U.S." Paxson said.

Aside from the immigration ban, the U.S. Citizenship and Immigration Services announced earlier this month that it will suspend the expedition of H-1B visa processing from April 3 onward, which Paxson said could mean graduating international students may find it harder to get jobs.