Asian-American civil rights groups and parents filed suit Thursday to block New York City from launching its plan to diversify eight top high schools by giving more seats to applicants who miss the test-score cutoff for admission.

Mayor Bill de Blasio aims to give 20% of the seats to students who almost reach the qualifying scores on an entrance exam for Stuyvesant and seven other specialized high schools.

Filed in federal court in Manhattan, the antidiscrimination suit says the mayor’s initiative disproportionately hurts Asian-American students’ access to these sought-after schools and violates their equal-protection rights. Currently, 62% of students at these schools are Asian.

One of the parent plaintiffs, Yi Fang Chen, came to Brooklyn from China as a teenager speaking little English. Her mother was a seamstress, her father a construction worker. Ms. Chen earned a Ph.D. in statistics from Stanford University and is a data scientist with two young children who may want to attend these high schools.

“I feel like everyone deserves equal opportunity,” she said in an interview. “That is what this country is for, not equal outcomes.”