From left, Homeland Security Secretary John Kelly, Attorney General Jeff Sessions and Secretary of State Rex Tillerson offer remarks at U.S. Customs and Border Protection headquarters on President Trump’s reconstituted travel ban. (Mark Wilson/Getty Images)

University leaders greeted President Trump’s revised executive order on immigration with a mix of relief and deep concern Monday — relief that some provisions were eased from his January order, which had been frozen by the courts, and concern that its overall impact will damage the country’s longtime status as a destination for the world’s top scholars.

Trump signed the order Monday blocking the issuance of new visas for people from Libya, Syria, Iran, Somalia, Sudan and Yemen for 90 days; suspending the refugee program; and limiting the number of refugees who will be admitted annually. As with Trump’s previous order, some praised the ban for protecting national security, while others condemned it as an unconstitutional effort to keep Muslims out of the country.

University leaders had spoken out strongly against the initial executive order, which left some students and faculty members unexpectedly stranded in airports and other countries.

“Almost instantly our concern was for the chilling effect this has for international students to come to the United States and America’s ability to remain competitive,” said Lizbet Boroughs of the Association of American Universities. “If they’re not coming here, they’re coming to Canada, to the United Kingdom and other countries.”

She said universities were pleased that one country, Iraq, was removed from the list. “And the delayed implementation will ensure none of our students are caught in transit, as they were in January.” But overall, she said, schools were in a watch-and-wait mode, worried about the effect on future enrollment and faculty recruitment.

Darrell G. Kirch, who leads the Association of American Medical Colleges, said in a statement that they are deeply disappointed that the revised order does not “explicitly recognize the importance of international medical graduates, physicians, and medical researchers to the nation’s health security,” and asked for waivers and other allowances for health professionals from those countries, including international medical graduates who are to be matched to residency programs on March 17, and who are required to begin treating patients in July.

Kirch wrote that the United States relies on international medical graduates for a significant portion of patient care and that such graduates go through rigorous screening as part of the visa process. “In addition, international scientific researchers and post-graduate trainees are important to medical research,” he wrote, “conducting ground-breaking work that leads to cures and effective therapies for patients in the United States and around the world.”

The organization hopes to work with the administration to ensure that doctors and scientists who have been screened are not prevented from entering and remaining in the United States. “Failure to further clarify this order will not only have short-term negative implications, but will have a lasting impact on our nation’s patients, particularly those in rural and urban underserved areas.”

At Princeton University, hundreds of people attended a “day of action” Monday designed to teach and mobilize response to Trump’s policies, including the executive order on immigration.

Mary Sue Coleman, the president of the Association of American Universities, said in a written statement that they are hopeful that the executive order will cause less disruption than the previous ban. “The new exemption for current visa and green-card holders from the six affected countries means that students and faculty already on university campuses can, for the most part, leave the country and reenter without being automatically prevented from returning. We are also pleased that the new order provides for a case-by-case waiver process for individuals from these six countries and specifically cites study and work as circumstances in which case-by-case waivers might be appropriate.”

She noted that AAU schools have worked closely with the federal government to help protect the country and will continue to do so.

But while agreeing with Trump that national security is essential, “we remain concerned that the new order, like its predecessor, poses a fundamental long-term threat to America’s global leadership in higher education, research, and innovation.” The order, among other things, would still limit entry for thousands of students and faculty members.

“Perhaps most alarmingly,” she wrote, “this order conveys the same damaging message to talented people from the six affected countries, as well as others: you are no longer welcome here. This message is especially clear in the absence of a statement by the President that America needs to remain the destination of choice for the world’s most talented students, scientists, engineers, and scholars.”

“Our country’s economic competitiveness and global leadership would not be possible without the extraordinary flow of international talent that has been drawn here for many decades by academic opportunity and American values. Actions that place our values and our status in doubt are likely to cause serious lasting harm.”

The president of the Association of Public and Land-grant Universities, Peter McPherson, said in a statement that while the new order is more limited in scope than the previous one, the impact is significant: More than 15,000 students and 2,000 scholars from the six countries included in the ban studied and did research at U.S. universities in 2015-16. And the pipeline of new students, many of them in the midst of the application process, he noted, is now cut off.

U.S. universities excel, in part, because of their ability to connect throughout the world, he said, but the order undermines that. All six of the U.S.-based  2016 Nobel Prize winners in economics and scientific fields were born abroad, he noted, and international students contribute billions to the economy.

Molly Corbett Broad, the president of the American Council on Education, said the group welcomes the effort to clarify the earlier version and called the order a step in the right direction of safeguarding the country “while still ensuring that the United States remains the destination of choice for the world’s best students, faculty and scholars, regardless of their nationality.”

But, she added, “while the revised order has narrowed the number of people impacted by the travel ban, we fear that those still excluded — coupled with the faulty initial roll-out and the harsh rhetoric that often accompanies today’s public policy discussions about immigration — still creates a climate where it is far more difficult for international students and scholars to view this country as a welcoming place for study and research.”