International enrollments at American colleges have fared better than expected this year, but many schools still fear the political climate in the United States, according to a national survey.

The Institute of International Education reported yesterday that the number of new students coming from abroad fell by an average of 7 percent at nearly 500 colleges and universities surveyed this autumn, but said the results from school to school were more mixed than many had feared.

Many schools nevertheless have concerns about the US political climate and fear that it could drive students away.

While 45 percent of schools saw declines in international enrollment, nearly a third said their numbers had increased since last year, the survey found. The remaining 24 percent said they saw no change.

“It’s definitely a wake-up call, but by no means is it a crisis, and it does not come anywhere close to the precipitous decline and plummeting of numbers that the entire sector had been predicting,” said Rajika Bhandari, head of research, policy and practice for the nonprofit group based in New York.

The White House’s proposed travel bans and separate reports of violence against immigrants had fueled fears of a sharp decline in students coming from abroad. The anxiety spurred many campuses to boost their recruiting efforts, while some launched marketing campaigns meant to make foreign students feel welcome.

Despite the improved outlook, the survey found that half of the 500 colleges still worry America’s atmosphere could discourage potential students, and 20 percent reported that the climate has already led some students to leave.

“We don’t know what the trends are going to look like for next year, but for sure there are concerns,” Bhandari said.

The survey offers only a preview of this year’s trends and was released alongside the institute’s annual “Open Doors” report, which tracks international students at 3,000 US schools but lags a year behind.

The broader survey covering the last school year found that US colleges hosted a record number of international students but also saw new enrollment fall 3 percent since 2015, the first decrease in at least six years.

Students from China and India made up nearly half of all international students last year, reaching a combined 530,000. Their numbers have continued to grow, but at a much slower rate than in previous years. Iran, the only nation in President Donald Trump’s travel ban with heavy numbers of students in the US, sent 12,600 students there last year, an increase of about 3 percent.

The top states for international students remained unchanged, with California topping the list followed by New York, Texas and Massachusetts.

The report found that the number of Americans studying abroad grew by about 4 percent, marking another year of slow but steady growth.