Even proponents of gifted education say New York’s current admissions system is flawed and offers advantages to parents who have the savvy and the resources to navigate the confusing process.

“New York has had one of the worst histories on this issue,” said Gary Orfield, a prominent researcher on school segregation and the co-director of the Civil Rights Project at the University of California, Los Angeles. “If you want to do anything except give special advantages to people who already have special advantages, tests aren’t the way to do it.”

Mr. de Blasio’s school diversity panel recommended that the city replace its elementary gifted programs with magnet schools and enrichment programs that do not require exams for entry. The city should also scrap most academic prerequisites for admission into middle schools, the group said.

It may take the mayor months to issue a decision on the proposal. But even if he doesn’t eliminate gifted classes altogether, which would amount to a seismic change for the district, he almost surely will face pressure to change how young children gain entry into the programs.

Mr. de Blasio has spent much of the last year railing against the city’s practice of using a single standardized test to determine entry into its elite high schools, which enroll tiny numbers of black and Hispanic students.

Though the specialized school exam has kindled a fiery uproar about race, class and opportunity in New York, the more obscure test that sorts 4-year-olds each year into gifted schools could force a broader reckoning.