NEW HAVEN, Conn. — A major increase in international enrollment in recent years has intensified the competition for entry to America’s top private colleges and universities, as ever-growing numbers of applicants angle for the limited number of seats.

That tension is particularly evident in the eight prestigious Ivy League schools: Federal data shows that their freshman classes grew slightly from 2004 to 2014 – 5 percent – while the number of incoming foreign students rose 46 percent. At the same time, applications to the schools shot up 88 percent.

At Yale University, where just 6 percent of 30,000 applicants are accepted, the foreign share of the freshman class has grown from single digits to 11 percent. As Yale’s undergraduate enrollment has edged upward since 2004, foreigners have accounted for almost all of the growth, reflecting a deliberate strategy to deepen Yale’s engagement with the world.

“We want to bring together an incredibly diverse student body – diverse in every way,” said Jonathan Holloway, dean of Yale College. “If we want to train the next generation of global leaders, we better have the globe here.”

Foreign and domestic demand grew so high that Yale has embarked on its biggest expansion since its undergraduate college opened to women in 1969. Next fall, Yale will open two new residential complexes, a $500 million project to lift enrollment capacity 15 percent.

International growth has fostered an increasingly cosmopolitan culture on campuses across the country, with academic benefits for domestic and foreign students alike. It gives colleges an additional path toward ethnic and racial diversity, opening doors to students from Africa, Asia, Latin America and Europe. But it also injects pressure into the admissions scramble that U.S. high school seniors are starting to experience this month as schools release early-admission decisions.

Charles Deacon, dean of admissions at Georgetown University, said he is concerned that international enrollment could be nearing an unacceptable level at some schools by potentially crowding out qualified U.S. students.

“We’re in a global world,” Deacon said. “There certainly is an argument for the presence of foreign nationals at U.S. universities. But is there a tipping point where this is too many? That is an issue we have to reckon with.”

The international share of freshmen at Georgetown rose from 3 percent in 2004 to 11 percent in 2014, on par with Yale. During that time, Georgetown’s admission rate fell 5 points, to 17 percent. Deacon said those numbers are reasonable for a university in the nation’s capital with a school of foreign service and a global profile.

“We think it works well for us,” he said.

U.S. applicants to elite schools are largely unaware of the growth of international enrollment and what it could mean for their chances, said Bruce Vinik, an admission consultant in Montgomery County, Maryland. He said the subject could draw “pretty strong” reactions from students anxious about whether their top-choice schools will accept them.

“Some kids would probably be upset it has increased competition and made it tougher to get into these colleges,” he said.