Mayor Bill de Blasio’s push to better integrate New York City’s specialized high schools was met with fierce pushback but also pledges of support after the mayor announced Saturday he would work to overhaul admissions at the elite schools.

The reaction foreshadows the battle that lies ahead if de Blasio is going to convince lawmakers to sign off a key piece of his plan.

Considered the Ivies of the city’s high school system, eight of the nine specialized high schools admit students based on the results of a single entrance exam (the remaining performing arts school requires an audition.) The most significant but controversial change de Blasio is proposing is to scrap the test in favor of a system that offers admission to top students at every middle school, which requires a change in state law for some of the specialized high schools.

Many alumni from those schools have fought fiercely to preserve the entrance exam requirement, worrying that changing the admissions rules will lower academic standards.

Many made the familiar arguments that the city should instead focus on improving the quality of middle schools, or expand access to gifted programs, to serve as a feeder into top high schools.

Alumni who would like to see the Specialized High School Admissions Test remain in place likely have many lawmakers on their side. New York State Senator Toby Ann Stavisky, a Democrat who represents several Queens neighborhoods, released a statement that she “couldn’t disagree more” with the mayor’s proposal.

The reaction also captured concerns about how the changes could impact Asian students, who make up a disproportionate share of enrollment at the specialized high schools. Those students are also likely to come from low-income families.

But others took to social media to support the mayor’s proposal. Specialized high schools have enrolled an increasingly shrinking share of black and Hispanic students: While two-thirds of city students are black or Hispanic, only about 10 percent of admissions offers to those schools go to black or Hispanic students.

Some thanked the mayor for taking action after campaigning for years to make changes.

And not all alumni were against the changes. Also included in the mayor’s plan is an expansion of Discovery, a program that helps admit low-income students who just missed the cutoff score on the entrance exam.