But the vast majority of those who signed the letter — including Madeleine Albright and John Kerry, the former secretaries of state; Michèle A. Flournoy, the former under secretary of defense; and Susan E. Rice, the former national security adviser — rose to senior security jobs in government under Democratic presidents.

Their argument mirrors one also being made by states that claim the revised travel ban discriminates against Muslims and will hurt businesses and universities.

A week after taking office, Mr. Trump issued an executive order to suspend the nation’s refugee program as well as travel from seven predominantly Muslim countries to give the government time to install rigid security vetting of immigrants. The order created chaos at American airports nationwide and was blocked by a federal appeals court.

This week, the Trump administration issued a new order that slightly scaled back the original ban but is still considered a significant hardening of American immigration policy.