For years, New York City has essentially maintained two parallel public school systems.

A group of selective schools and programs geared to students labeled gifted and talented is filled mostly with white and Asian children. The rest of the system is open to all students and is predominantly black and Hispanic.

Now, a high-level panel appointed by Mayor Bill de Blasio is recommending that the city do away with most of these programs in an effort to desegregate the system, which has 1.1 million students and is by far the largest in the country.

Mr. de Blasio, who has staked his mayoralty on reducing inequality, has the power to adopt some or all of the proposals without input from the State Legislature or City Council. If he does, the decision would fundamentally reshape the segregated school system and reverberate in school districts across the country.