There were more than 360,000 Chinese students in the United States in the 2017-2018 school year

China's warning Monday about the "risks" to students of coming to the United States could pose a major challenge for U.S. higher education because China is the largest source of international enrollment for America's colleges and universities.

There were more than 360,000 Chinese students in the United States in the 2017-2018 school year, according to the Institute of International Education, more than triple the count from nine years earlier. U.S. schools benefit from the tuition they pay, educators say, and the global perspective they add to campuses.

But the flow of students has drawn scrutiny from the Trump administration and lawmakers wary of China. Officials have questioned whether Chinese-sponsored Confucius Institutes based on college campuses - which promote Chinese language and culture - represent an espionage threat. Meanwhile, there are reports that the State Department has tightened review of Chinese applications for student visas. And tensions between China and the United States have arisen over tariffs and trade disputes.

On Monday in Beijing, Chinese education official Xu Yongji lamented what she called the politicization of "normal China-U.S. educational exchanges." Xu said the government is advising students to "strengthen" their risk assessments before deciding to study in the United States.

A State Department official, who spoke on the condition of anonymity, said in an email the United States "rejects the unfounded allegation of a widespread and baseless campaign to deny Chinese visas." The official added, "We welcome Chinese students and scholars to the United States to conduct legitimate academic activities."

Colleges are scrambling to understand how the frictions could affect their enrollment.

"All college and university presidents want to have an internationally diverse campus because our students are going to exist in a globalized world," said Terry W. Hartle, senior vice president for the American Council on Education, a higher-education group. "But for a number of reasons, there are more concerns about international students enrolling at colleges and universities than I remember in the last 25 years."

Hartle added: "Campus officials are worried that international students could become pawns in a trade war."

George Washington University enrolls several hundred Chinese undergraduates, about half of international enrollment at the private university. "They contribute in more ways than just revenue," said Costas Solomou, GWU's dean of admissions. "Our Chinese students do incredibly well."

As of Monday, 10 Chinese students who had been admitted and had submitted deposits to enroll in GWU's next freshman class have backed out of those plans, Solomou said. That's higher than the usual attrition. He said he is hearing similar reports from other schools. "We're all nervous about this," he said.

John Latting, dean of admission at Emory University, which has a large cohort of foreign students, said in an email: "The presence of excellent Chinese and other international students and scholars on campus enhances our ability to deliver the best possible educational opportunities to all our students. We have been on the ground recruiting top students in China since the 1990s, and our enrolling classes of today benefit from the mutual trust we have developed over the many years."

The impact of curtailing Chinese enrollment would vary widely. While the most selective schools would hate to lose exceptional talent from China, others are worried about the stability of a key source of tuition revenue.

At Colgate University, about a third of the 75 or so international students in each class are from China, said Jamiere Abney, senior assistant dean of admission. He said college officials are well aware of the financial hit some schools would face with a loss of Chinese students. He could readily see the potential loss to campus culture. "Something like this, a political thing outside our control, can definitely impact us in a unique way," Abney said.

Pomona College has dozens of Chinese students. "If we claim to have the best educational system in the world, then we have to be competitive globally," said Pomona President Gabrielle Starr, "and not just drawing students from our own backyard or across the United States." She said the Chinese add to "diversity of thought and culture" on campus.

For the University of California at Berkeley, the 1,460 undergraduate and 988 graduate students from China are by far the largest group of international students. School spokesman Dan Mogulof declined to speculate on potential impact but said "as a university which values diversity - in the broadest sense and every form - Berkeley believes that having a global student population is a foundational element of our institutional character and academic mission. So, in that context we will continue to ensure that every student on this campus, regardless of their country of origin, feels safe, respected and welcome."

Mary Sue Coleman, president of the Association of American Universities, said the United States has long been able to recruit the best and brightest from all over the world. The notion that the country is unwelcoming could be damaging, she said.

Because so many of the international students come from China, she said, "the impact of having these students turn away would be pretty dramatic."

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The Washington Post's Anna Fifield in Beijing contributed to this report.