HARTFORD, Conn. — Seven African-American and Hispanic families sued Connecticut and Hartford officials on Thursday, saying race-based student quotas at high-performing city magnet schools are unconstitutional and have kept their children from attending.

Eight parents from Hartford filed the lawsuit in federal court on behalf of their 19 children. The lawsuit says hundreds of student seats in the 21 magnet schools are unfilled because too few white children are enrolled. The schools are limited to 75 percent minority student enrollment under the landmark Sheff versus O’Neill school desegregation case in state court.

The families say their children have not been able to get into the magnet schools under a lottery system and have been forced to attend low-performing, more segregated schools. The lawsuit also alleges the lottery system is unfair because it favors white and Asian students. They’re seeking an end to the quota so more city children can attend the schools.

State and city officials declined to comment Thursday. They said they hadn’t seen the lawsuit and generally do not discuss pending litigation.

“The state of Connecticut and Hartford Public Schools have decided to close the doors to Hartford’s elite magnet schools to my children because they are black,” said Lashawn Robinson, a mother of five and one of the plaintiffs in the lawsuit. “This case is about my children’s future, and my children’s rights, but it’s also important for all students of all races. Their race should not be a disadvantage to their ability to receive a quality education.”

Robinson said she tried to get her oldest son Jarod, now 19, into a magnet school since he was 3, but was unsuccessful in the lottery program. Jarod said he had hoped to get into a performing arts or aerospace and engineering magnet school.

“It’s unfair,” he said. “They have stuff that that other schools don’t have and I wanted to experience those things.”

The lawsuit was filed with the help of the California-based Pacific Legal Foundation, a nonprofit legal group that advocates for individuals’ rights and limited government.

Joshua Thompson, a senior attorney with the foundation, said the U.S. Supreme Court has held for 40 years that racial quotas are unconstitutional. He said his group is prepared to take the case to the nation’s highest court if need be.

“This quota is so rigid, inflexible and unconstitutional that Hartford magnet schools have to leave desks empty if enrolling a black child would upset that quota,” he said during an announcement of the lawsuit outside the state Capitol. “It is outrageous that in this day and age there would still be policies on the books that turn children away from the school of their choice because of the color of their skin.”

State officials tried last year to increase the minority cap in the magnet schools to 80 percent, in an effort to fill empty desks. State officials said raising the cap would have allowed nearly 1,200 additional minority students from Hartford to attend the magnet schools. About 3,600 students were on a waiting list for magnet schools and other school choice programs last year.

But a state judge overseeing the Sheff case rejected the request, citing the increased segregation it would create.

There are about 21,000 children in the Hartford school system. About 53 percent are Hispanic, 31 percent are black, 11 percent are white and 3 percent are Asian.

About half the city’s children are educated in traditional public schools, which serve disproportionately more students from disadvantaged backgrounds, have lower graduation rates and have high racial isolation.