President Trump speaks in the Roosevelt Room of the White House in March 2017. (Evan Vucci/AP)

This article has been updated.

The roster of new international students at colleges and universities fell more than 6 percent in the past school year, according to a report made public Tuesday, renewing questions about whether President Trump’s nationalist rhetoric and policies have undercut overseas demand for U.S. higher education.

That finding is double the previous rate of decline. What’s more, schools are reporting that the flow of international students is continuing to shrink this fall. Preliminary data from the nonprofit Institute of International Education show a 1.5 percent drop in new international students arriving on U.S. campuses in the current school year. That marks a third straight year of contraction on a key measure of academic exchange.

Many schools attributed the trend to problems with student visa delays and denials, according to the institute, as well as the U.S. social and political climate and student decisions to enroll outside the United States.

The new data elicited a worried response from the president of George Mason University in Northern Virginia and from other higher-education leaders in the Washington region and nationwide.

“While other countries work hard to attract international students, we are managing to send a message that talented foreigners are not welcome here, just when we most need them,” Ángel Cabrera, president of George Mason, said in a statement responding to the report.

Colleges rely on international students for the tuition they pay and the diverse perspectives they bring.

Many factors influence where foreign students go to school, including the cost of coming to the United States and the growing capacity of higher education systems abroad. But some education leaders say Trump’s advocacy of immigration restrictions, travel bans and a U.S.-Mexico border wall is not helping the nation compete for academic talent in the global market.

At George Mason, Virginia’s largest public university, 8.5 percent of roughly 37,700 students this fall are international. The total has grown steadily in recent years, and university officials want to ensure that it does not recede. Cabrera said foreign students bring hundreds of millions of dollars a year to Virginia’s economy and pay higher out-of-state tuition rates at public institutions, helping to subsidize the education of state residents.

Trump administration officials say the United States remains committed to recruiting and hosting international students. They point to data showing that total international enrollment in the 2017-18 school year reached an all-time high of nearly 1.1 million students, up 1.5 percent from the year before. That figure counts new and continuing students. The total grew because some of the continuing international students remained longer than in years past.

But the total number of new international students — including undergraduates, graduate students and others who are not seeking degrees — was about 272,000. That was down 6.6 percent from the year before and nearly 10 percent from the recent high of about 301,000 in 2015-16.

The institute’s annual report, known as Open Doors, is funded by the State Department.

Caroline Casagrande, deputy assistant secretary of state for academic programs, told reporters in a conference call that multiple factors explain the drop in new enrollment. She also traced the trend back to decisions potential students were making about college applications in 2014, well before Trump took office.

“It’s quite frankly unwarranted to say it’s completely the results of a political environment,” Casagrande said, according to a transcript of the call.

Marie Royce, assistant secretary of state for educational and cultural affairs, said Tuesday at the National Press Club that the United States wants to send a message: “America’s academic doors are open and welcoming” to students throughout the world. She said that the nation remains the top destination for international students and that the two-way relationship of student exchange is beneficial for national security.

Allan E. Goodman, the institute’s president and chief executive, said global competition for students is intensifying.

“We’re not hearing that students feel they can’t come here,” Goodman said. “We’re hearing that they have choices. We’re hearing that there’s competition from other countries, and that, in this very sophisticated, very competitive market for the first time, we have real competition.”

At some universities, international enrollment remains stable.

Robert Groves, provost of Georgetown University, said the Jesuit institution in Washington has not detected any decline in overseas demand. But Groves said he worries that dwindling foreign enrollment could hurt colleges that are struggling to fill seats. “When they hurt, all of us hurt in a real way,” he said.

New York University had about 17,500 international students in the past school year, the report found, more than any other. MJ Knoll-Finn, NYU’s senior vice president for enrollment management, said the total held steady this fall.

NYU officials have taken extra steps recently to ensure those students feel welcome, she said. Faculty members and administrators check in with each one after arrival to see if they have any concerns. “The culture for them can feel unwelcoming,” Knoll-Finn said. “We have to do a lot of work to make sure they know that we want them here.”

At the University of Florida, Provost Joe Glover said there was a precipitous drop this year in international master’s students in engineering. Enrollment fell by a few hundred students, he said, causing a significant budget challenge.

“We don’t know the exact cause,” he said. “We are trying to reassure the international market that the university remains committed to providing these programs — and that the university is a welcoming environment.”

Soon after Trump took office in January 2017, he issued a ban on travelers from several Muslim-majority countries. That upended plans for some students and others seeking to enter the United States. The ban was challenged in court and subsequently revised.

Other administrative proposals and actions, including the phaseout of an Obama-era initiative that protected certain classes of immigrant students from deportation, have contributed to concerns among international students. State Department officials have sought to assuage those concerns, saying the department recognizes that international education is important for the U.S. economy and helps expose Americans to international issues and diverse cultures.

But higher education leaders say the United States must do more to stay competitive with countries such as Canada and Australia.

“The concerns about the political climate remain,” said Brad Farnsworth, vice president of internationalization and global management for the American Council on Education. That group represents college and university presidents. “This is really a global market now for international students, where they have a number of attractive options.”

Read more:

Report finds fewer new international students on U.S. college campuses

The Trump effect in college admissions: Rural outreach increases, international recruitment gets harder

‘I’ll be in Canada.’: More students are looking to head north

Libyan student, banned from entry to the U.S., is able to return to George Mason

Yale professor worries his wife and baby won’t be allowed back from Iran