In 2018, when Mr. de Blasio proposed a plan that would discard the exam and overturn the law, known as the Hecht-Calandra Act, he called the paltry numbers of black and Hispanic students in the specialized high schools “a monumental injustice.”

“Can anyone look the parent of a Latino or black child in the eye and tell them their precious daughter or son has an equal chance to get into one of their city’s best high schools?” the mayor asked.

Opponents of the mayor’s plan have said it could water down the schools’ academics and that it discriminates against Asian students, who would lose about half their seats at specialized schools under his plan.

“We firmly oppose the amended bill that completely eliminates the test and substitutes unnamed subjective criteria,” said the leaders of the Stuyvesant and Brooklyn Technical High School alumni associations, in the wake of Mr. de Blasio’s proposal.

A half-century after Hecht-Calandra passed, Mr. de Blasio has tried to make the case for why state legislators should eliminate it. But that plan has scant political support in Albany or downstate.

But both supporters and critics of the mayor’s plan have pushed him to release a blueprint to integrate all of the city’s 1,800 schools, not just eight especially prominent ones.

No proposal has materialized.

In 1977, a Times reporter observed that, after a decade of advocacy and discussion, the prospect of school integration in New York was dimming.

“If the dream of racially integrated public schools is slipping away now in much of New York City, what will have become of it five years from now, or ten years? The outlook, at best, is uncertain and troubled.”