“I refuse to believe there are only 19 brilliant African-Americans in the city; it simply cannot be the case,” Mr. Hewitt said. “It is a shameful practice and it must be changed.”

The test-only rule has existed for decades, as have complaints about its effect on minority enrollment. In May 1971, after officials began thinking about adding other criteria for admission, protests from many parents, mostly white, persuaded the State Legislature to enshrine the rule in state law.

Mayor Michael R. Bloomberg said at a news conference on Thursday that the schools were “designed for the best and the brightest” and that he saw no need to change the admissions policy or state law.

“I think that Stuyvesant and these other schools are as fair as fair can be,” Mr. Bloomberg said. “There’s nothing subjective about this. You pass the test, you get the highest score, you get into the school — no matter what your ethnicity, no matter what your economic background is. That’s been the tradition in these schools since they were founded, and it’s going to continue to be.”

A bill introduced in the Assembly last session sought to give the city power over admissions to the schools. But it was not brought to a vote, said Michael Whyland, a spokesman for the Assembly speaker, Sheldon Silver. “We’ll look at the issue and study it,” Mr. Whyland said. “Of course we want to make sure everyone has equal access to all our schools.”