Mayor Bill de Blasio’s push to integrate the city’s specialized high schools now faces a legal challenge, which could potentially disrupt the current admissions cycle to the elite schools.

On Thursday, Asian-American parents and community organizations filed a lawsuit claiming the city’s diversity plans unfairly hurt their children’s chances of getting into a specialized high school, the Wall Street Journal first reported.

The suit targets the city’s planned expansion of the Discovery program, which offers admission to students who scored just below the cutoff on the exam that is the sole entrance criteria.

The law firm representing the plaintiffs has also asked for a preliminary injunction while the lawsuit is pending. The Pacific Legal Foundation, a non-profit firm with conservative, libertarian leanings, argues that “the challenged plan will impact imminent admission decisions — i.e. this admissions season.” If an injunction were granted it could unsettle an admissions process already underway for the city’s current eighth graders, who took the test that determines admissions in October or early November.

The lawsuit arrives atop a wave of anger from some in the city’s Asian-American community, whose children make up a disproportionate percentage of the enrollment at specialized high schools. Citywide Asian students represent 16 percent of the student population but comprise 62 percent of those at the sought-after subset of schools.

Currently, Discovery participants are mostly Asian: This year, those students made up 64 percent of those admitted to specialized schools through the program.

The city is planning a two-year expansion of Discovery to eventually account for 20 percent of seats at each specialized high school. Officials are also tweaking the program so that, in order to qualify, students must come from a middle school where at least 60 percent of students are economically needy. By doing so, the city estimates black and Hispanic enrollment in specialized high schools will increase from about 10 percent to about 16 percent. Citywide, those students comprise almost 70 percent of enrollment.

But the lawsuit argues the changes are discriminatory and would disproportionately shut out Asian students. It also claims the program’s expansion would make it more difficult to get into a specialized high school by limiting the number of seats available to students who aren’t in Discovery.

“We all have the American dream of equal opportunity,” Yi Fang Chen, a mother who is part of the suit, said in a press release. But she said the changes to Discovery are like “taking someone else’s dream away.”

An education department spokesman did not comment directly on the lawsuit, but said the city’s plans would “expand opportunity and raise the bar” at specialized high schools.

“Our schools are academically stronger when they reflect the diversity of our city,” spokesman Will Mantell wrote in an email.

At a community meeting in Brooklyn to discuss the suit, Asian parents were encouraged to keep up public pressure on the city to help build support for their cause.

“We’re just here to fight for our rights,” one father said. “We want to be heard.”