Updated, 4:55 p.m. — The state is offering the city up to $10 million over the next three years to increase diversity at eight low-performing schools.

The pilot program, announced Tuesday, asks the city to come up with ways to attract students from higher-income families to eight schools on the state’s list of low-performing “focus” and “priority” schools. Each school will be eligible for up to $1.25 million to implement new dual-language, arts, Montessori, or other specialty programs, develop new admissions policies, or come up with other ways to increase socioeconomic diversity.

The announcement — likely to be State Education Commissioner John King’s last before he leaves for a post at the federal education department — reflects King’s longtime concern that the city’s admissions and enrollment policies concentrate high-needs students in struggling schools. A March analysis found that only 25 percent of black and Latino students in the city attended schools that could be considered “multiracial.”

“The world is a diverse place; our students shouldn’t be isolated because they come from struggling neighborhoods,” King said Tuesday.

The city has until Feb. 13 to choose schools and apply for the grants, which come from federal School Improvement funds. A spokesman for the State Education Department pointed to Connecticut’s magnet schools initiative and to diversity-boosting efforts in Brooklyn’s District 13 as models for programs that could be expanded with the new funding.

“We hear so often that this is such difficult problem, that there are no easy solutions,” said David Tipson, the director of New York Appleseed, a group that advocates for policies to increase school diversity. “I think this shows that addressing this issue head on, proactively, is not all that difficult. I think we see here what can happen when school officials decide they want to do something.”

Department spokesman Harry Hartfield called the grants “a great opportunity” and said the city looked forward to applying. The city expects to have some programs in place by September 2015.

Statewide, another 17 schools are eligible. Here’s the information the state has released about the program.