The gradual elimination of the existing program will remove a major component of what many consider to be the city’s two-tiered education system, in which one relatively small, largely white and Asian American group of students gain access to the highest-performing schools, while many Black and Latino children remain in schools that are struggling.

New York, home to one of the most racially segregated school systems in the country, is more reliant on selective school admissions than any other large system in America.

The move represents one of Mr. de Blasio’s most dramatic actions to combat segregation in city schools, though it also puts New York more in line with how other cities are approaching their own segregated gifted classes. About 75 percent of the roughly 16,000 students in gifted elementary school classes in New York are white or Asian American. Those groups make up about 25 percent of the overall school system.