The president of Portland State University, Wim Wiewel, met last week with 10 prospective students in Hyderabad, India. But what started as a get-acquainted visit quickly turned into more of a counseling session, as the students expressed fears about coming to the United States this fall.

One student, who is Muslim, said his father was worried that the United States had an anti-Muslim attitude, Wiewel recounted. “Several others said they were concerned about the ‘Trump effect,’” he said in an email.

“I’d say the rhetoric and actual executive orders are definitely having a chilling effect,” Wiewel wrote, referring to the Trump administration’s travel ban.

Like many universities across the country, the Oregon university is getting fewer international applications.

Nearly 40 percent of colleges are reporting overall declines in applications from international students, according to a survey of 250 colleges and universities, released this week by the American Association of Collegiate Registrars and Admissions Officers. The biggest decline is in applications from the Middle East.

Many officials cited worries among prospective students about Trump administration immigration policies. “International student recruitment professionals report a great deal of concern from students all over the globe,” the study said.

On Wednesday, the federal judge in Hawaii who blocked the latest version of the administration’s travel ban cited the financial harm the executive order posed to the state’s university system, which recruits students and hires faculty members from the six target countries. (Washington state officials raised similar concerns in successfully challenging the first travel ban.)

Graduate schools appear to be feeling the worst pinch, with nearly half reporting drops. “Our deans describe it as a chilling effect,” said Suzanne Ortega, president of the Council of Graduate Schools.

The numbers — while not yet final — are provoking anxiety in some programs that rely on international students, who bring more than $32 billion a year into the U.S. economy. International enrollment at U.S. colleges has been on the rise during the past decade, and for the first time exceeded 1 million students last year.

Still, despite the steady increase, the movement of students from one country to another is sensitive to fluctuations tied to political and economic forces. So some officials cautioned that a “Trump effect’ is just one possible explanation for this year’s application figures. Beyond that, many schools, including New York University, the University of Southern California and Northeastern University, reported that their international numbers are up. Purdue University reported a 1.2 percent decline in graduate school applications.

Wiewel made his trip to Hyderabad not long after residents of the city held funeral services for a young Indian man who was killed in a bar in Olathe, Kansas, where he worked as an engineer. The shooting is being investigated as a hate crime.

Wiewel reassured the students — all admitted to Portland State’s graduate engineering program — that his school’s environment was safe and welcoming. He was a bit surprised by their concerns, he said, because students he visited earlier in New Delhi and Bangalore had been more anxious about financing their graduate studies, apparently a reaction to India’s recent currency shortage. Other economic factors may also be involved in the application declines, Ortega said, including crude oil prices in Saudi Arabia.

Also at play: uncertainty about the future of a visa program called H-1B that international graduates frequently rely on to remain in the United States to work.

For several graduate schools, the Trump administration’s travel ban, which initially affected seven predominantly Muslim countries, could not have been more poorly timed. It was announced in late January as deadlines loomed for applications to some graduate programs, and it came on the heels of Donald Trump’s virulently anti-immigrant rhetoric during the campaign.

Slumping graduate school applications can be seen at universities ranging from giant Big Ten public universities like Ohio State and Indiana University to regional programs such as Portland State, a school of just over 27,000 students, including more than 1,900 international students.

At Indiana University, international applications for undergraduate programs increased 6 percent, but graduate applications for some programs are posting big drops, said David Zaret, vice president for international affairs.

Zaret said international applications to the masters program in business were down 20 percent, and down 30 percent in both the master of law program and at the School of Informatics and Computing. The university will not have problems filling the programs, but the drop might affect the overall quality of the applicant pool, he said.

Ohio State has also seen an increase in international undergraduate applications but a significant overall drop — 8.4 percent — in international applicants to its graduate programs, a university spokesman, Chris Davey, said. The biggest decline was among students from China — a fact Davey said did not support the “Trump effect” theory. In 2016, he said, there were 2,412 graduate applications from China; this year the number was down to 1,952.

“We’re inclined to say that the overarching factors that might be influencing this are probably global economic factors and it would be premature to conclude that it’s the travel ban,” Davey said. “But it certainly could be.”

Because application deadlines at several larger schools had passed before Trump’s travel ban was announced, some universities are more worried about the “yield” — the number of students offered admission who end up enrolling, said Frances Leslie, vice provost for the graduate division at the University of California, Irvine.

Applications at Irvine are not down, but students have expressed concerned about coming to the United States, Leslie said. “We’re hearing from students, even beyond the seven countries, expressing concern,” Leslie said, referring to Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen, which were singled out in the first travel ban. “This year, even when students are admitted, they may not be willing to accept the offers.”

The university will not have those numbers until April 15, a national deadline for students to make a decision.

At Portland State, where undergraduate international applications are up 4 percent but international graduate applications are down 15 percent, the school’s vice provost for international affairs, Margaret Everett, said she had heard recently from a Chinese student who canceled his application, citing the political climate.

“Obviously we’re concerned about the climate and the rhetoric and the administration policies and travel ban,” Everett said.

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