University of Washington students walk on the Seattle campus in 2012. Campuses nationwide are reporting a decline in the number of newly enrolled foreign students. (Elaine Thompson/AP)

The flow of new international students entering U.S. colleges and universities shrank last year and has continued to decline this fall on many campuses, breaking a recent trend of growth, a nonprofit group said Monday.

The data from the Institute of International Education are likely to fuel questions about how the divisive 2016 presidential campaign and U.S. policy shifts since President Trump took office have influenced the global academic market.

Higher education leaders have been on alert for signs that the Trump administration’s efforts to ban travelers from certain majority-Muslim countries and heightened scrutiny of foreign visitors are deterring international students.

Allan E. Goodman, the institute’s president and chief executive, said it’s too early to conclude there has been a “Trump effect” on enrollment. Saudi Arabia and Brazil, he noted, recently scaled back government scholarship programs that had propelled many students to the United States. And total foreign enrollment at U.S. institutions — counting continuing students as well as new ones — reached a record high of 1.08 million in 2016. The total grew because some of the continuing international students remained enrolled longer than in years past.

But Goodman said he is struck by two questions he often hears when he travels abroad: Does everybody in America have a gun? And does everybody in America pay full price for college? Those issues arise in media coverage of U.S. gun violence and of the U.S. education sector, which relies heavily on affluent international students for tuition revenue. Safety and value, Goodman believes, are increasing priorities for foreign students.

“They’re not unreasonable questions,” he said. “They have nothing to do with whether you live in a red state or a blue state.”

The institute, in partnership with the U.S. State Department, tracks international enrollment at about 2,100 U.S. colleges and universities through an annual report called Open Doors. Except for a brief period after the Sept. 11, 2001, terrorist attacks, international enrollment at U.S. schools has grown consistently for decades.

Students from China account for nearly one-third of foreign enrollees in the United States. The Chinese total surpassed 350,000 in fall 2016, up 7 percent from the previous year. India ranked second, with 186,000 students in the United States last fall, up 12 percent. The Saudi student total fell 14 percent, to 53,000, and the Brazilian total fell 32 percent, to 13,000.

“International student exchange is an essential contributor to America’s economic competitiveness and national security,” Alyson L. Grunder, deputy assistant secretary of state for policy in the department’s Bureau of Educational and Cultural Affairs, said in a statement. “The U.S. higher education sector remains the global leader in welcoming students from around the world, and at the same time, we are committed to increasing opportunities to study abroad for Americans.”

But the Open Doors report found new foreign enrollment fell nearly 10,000 students in fall 2016, to about 291,000. The 3 percent drop was the first in the six years the report has published that statistic.

Separately, the institute teamed with 10 education groups on a snapshot survey of foreign enrollment this fall. About 500 schools responded, reporting an average decrease of 7 percent of new international students. That figure offers a preliminary and partial view. New foreign enrollment was up at many schools and down at others.

“I need to see another year of data,” Goodman said, to know what effect, if any, Trump has had.

The snapshot survey found colleges cite a mix of factors for this year’s decline, “including competition from other countries, the cost of U.S. higher education, visa delays or denials and an uncertain U.S. social and political climate.” Half of schools responding to the survey said they are worried about perceptions of the United States among international students who are considering enrolling next year.

Many colleges have sent top officials overseas this year to reassure incoming and potential students, and they have launched a social-media campaign called “#YouAreWelcomeHere.”

At the University of Florida, new international enrollment — mostly graduate students — fell this fall to about 1,270 students, from about 1,880 the previous year. That’s a decline of 32 percent.

UF Provost Joseph Glover said engineering and business programs were hit hard, with a significant decline in new students from India. Glover said university officials have heard of similar drops elsewhere.

“If it represents the beginning of a downward trend, that could represent a serious problem for the nation,” Glover said. “It’s something that we’re watching with great concern.”

Rahul Choudaha, an executive vice president at StudyPortals, a Netherlands-based online search platform for international students, said market forces were causing enrollment shifts well before Trump’s presidential campaign. But he said Trump’s victory and actions in office have influenced many overseas who are attracted to U.S. schools but worried about their career prospects after graduation.

“The tightening of the immigration process is really posing some concerns for international students, especially at the graduate student level,” Choudaha said. Still, the United States remains a powerful educational draw. “There is a huge diversity of options in the U.S.,” he said. “A lot of these options are very high quality. It’s unparalleled.”