Riding on New York City’s popularity as a destination among Americans and tourists from around the world, New York University is seeing an increase in applications this year the scale of which it has not seen since before the terrorism attacks of September 11, 2001.

More than 37,000 high school seniors applied to NYU this year, up by nearly 3,000 from last year, the university announced yesterday. Students applying from outside America accounted for a substantial part of that rise, about 400 students, the university’s associate provost for enrollment management, Barbara Hall, said. Officials said the rise cements NYU’s position as the most applied-to private college in the country.

Universities across the country are reporting record numbers of applications this year, in keeping with a college market that has been tightening for several years. More high school seniors are applying to college than ever before, and there are more high school seniors than ever.

NYU’s jump this year is dramatic even by the university’s own standards. Applications to NYU have more than tripled in volume in the past 15 years, but university officials said they had gone eight years without seeing this large an increase.

“It’s much more than what I would have expected,” Ms. Hall said.

Other New York City colleges are also seeing a rise in interest. Columbia University is tallying its applications, but the current count, 22,249, is already higher than last year’s by more than 1,000 students, a spokesman, John Tucker, said.

The president of the New School, Robert Kerrey, said his school is also expecting a record year. He would not provide exact numbers, but said the university’s undergraduate liberal arts college, Eugene Lang, would see an 8% or 9% rise in applications, the same as NYU.

Mr. Kerrey said demographics are not the only factor. New York City, with its glistening new condominiums, rising incomes, and glamorous television portrayals, is one reason for the rise, he said. “Right after 9/11 this wasn’t a very good place to live. But the city has gotten more and more attractive,” Mr. Kerrey said.

At NYU, students and professors said the city’s television image has been a draw. Cell phone ring tones mimicking the theme music for the television show “Sex and the City” have been a standard for freshman girls, and “Sex and the City” tours of New York are common among freshmen, an NYU senior, Emily Frank, said.

Crime, by contrast, takes up just a small portion of the talk on tours for prospective students, Ms. Frank, who gives the tours, said. Though university officials refused to draw any contrasts, the new numbers could put NYU in a position to compete with Columbia.

Columbia’s acceptance rate is around 10%, compared to NYU’s 29% last year.

Ms. Hall said getting into NYU will be tougher than ever this year, as officials are not only receiving more applications but are also aiming to admit a smaller class. They are scaling back because officials last year underestimated students’ interest and accepted about 200 more students than there was room for, Ms. Hall said.