Seventeen leading universities, including all eight of those in the Ivy League, have added their support to a legal challenge to President Trump’s executive order on immigration, arguing that the order hinders their global mission and harms some individuals directly.

In some cases the impact was immediate, they argued, causing significant hardship for scholars: Six students and scholars at Princeton University were outside the country and unable to return when the ban was put in place, for example, and an additional 45 were unable to leave the United States. In some cases, the schools feared a future impact, as with the 150 applicants to graduate programs at Princeton who are from seven countries listed in the executive order, or the loss of academic conferences.

Trump vowed to keep radical Islamic terrorists out of the country when he signed a measure last month establishing a temporary ban on allowing people from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen to enter the United States, and a temporary suspension on allowing refugees to enter the country. “We don’t want them here,” he said. “We want to make sure we are not admitting into our country the very threats our soldiers are fighting overseas.”

Although many Americans support the ban as a means to institute more rigorous vetting, tighten the borders and make the country safer, others have protested that it violates fundamental national principles such as religious freedom by focusing on Muslim-majority countries.

Opponents quickly filed lawsuits, and a federal appeals panel upheld a ban on the order last week. People who had been blocked from entering the United States are now able to come.

Trump said Friday that he was considering rewriting the order, given the urgency of the situation. A spokesman for the White House did not respond to a request for comment Monday.

Meanwhile, challenges continued. Academic leaders have been extremely vocal in their opposition, with nearly 600 college presidents signing on to a letter of concern and tens of thousands, including 62 Nobel laureates, signing a petition. The amicus brief was filed in Monday in the U.S. District Court for the Eastern District of New York, supporting a civil action brought by the attorney general of New York and others.

Leaders of the schools — Brown, Carnegie Mellon, the University of Chicago, Columbia, Cornell, Dartmouth, Duke, Emory, Harvard, Johns Hopkins, the Massachusetts Institute of Technology, Northwestern, the University of Pennsylvania, Princeton, Stanford, Vanderbilt and Yale — argue that the order threatens their ability to attract the world’s best scholars and work across borders, and that it creates significant hardship for their students and faculty from abroad who had already undergone vetting to obtain visas.

They describe campuses that are increasingly international, with 16 percent of Columbia’s undergraduates this fall, for example, and 39 percent of its graduate students from overseas.

While some schools, such as Brown, Penn and Cornell, had single-digit percentages of their faculty from abroad, nearly one-third of Princeton’s faculty, and fully half of its academic professionals, visiting faculty and researchers this fall were international.

The brief argues that international diversity is important for the education of all students, that international scholars make important “scientific, technological, social, and political contributions to the United States and the world,” and it cited estimates that they contribute billions of dollars to the U.S. economy. It lists well-known academics who came to the United States from the affected countries, and it gives examples of faculty recruits and others who are now reconsidering joining the universities.

It ends with their belief that “safety and security concerns can be addressed in a manner that is consistent with the values America has always stood for, including the free flow of ideas and people across borders and the welcoming of immigrants to our universities.”