City University of New York’s ratcheting-up of admissions standards is its latest attempt to put its top-tier colleges in the same league as private universities such as New York University and Columbia.

The change pushes the minimum math SAT score required to get into CUNY’s top five colleges to 510 from 480, with a rise in English standards soon to follow, CUNY’s vice chancellor, Jay Hershenson, said.

“Public higher education in New York City should compete for the best and the brightest,” Mr. Hershenson said, adding that CUNY’s top-tier schools — Brooklyn, Hunter, Baruch, Queens, and City colleges — “are in the position to compete with any institution anywhere.”

In-state tuition at the five schools is just less than $4,400 a year; NYU and Columbia each charge more than $35,000 a year. The admissions change is reigniting a debate over how hiking standards affects the low-income students that are CUNY’s core demographic. The debate was raised in 1999, when the university raised standards at a set of designated “top-tier” colleges by slashing remedial classes and creating exit exams that students must pass before moving beyond sophomore year.

Proponents praised a bold attempt to raise achievement while critics complained CUNY was pushing out disadvantaged students.

Mr. Hershenson defended the change, saying CUNY’s standards push has raised enrollment and improved faculty quality without sacrificing racial and class diversity. Although 266 freshmen last year would have been pushed out under the new standards, he pointed out that all would have spots elsewhere in the CUNY system, including a free summer tutoring program.

The editor of the online magazine Inside Higher Ed, Scott Jaschik, said CUNY could reach the leagues of premier public colleges such as the University of Virginia and the University of Michigan without sacrificing its democratic mission. “The test is, does raising standards prompt changes that help everybody or not?” he said. Positive changes could include pushing New York City high school students to take harder math classes and pushing principals to improve their course offerings, he said.

Mr. Hershenson said CUNY would be working with 30 New York City high schools by 2015. He said the university has taken internal measures, too, such as working on new math curricula to bring students to speed.

An internal report on retention obtained by The New York Sun states that, while rates have improved in the last several years, as of 2006 just 44% of freshmen in four-year programs were graduating in six years.