Gubernatorial candidate Cynthia Nixon waded into the debate about racial diversity at New York City’s most prestigious high schools Thursday, saying she generally supports a plan that aims to boost their share of black and Hispanic students.

“We need them to be more racially diverse when it comes to black and Latino students,” Nixon said of the eight specialized high schools that use a test to admit students. “And we also need more lower-income students in those schools who are at the top of their classes, but may not have had the supports that would have propelled them into just testing in.”

When asked whether, as governor, she would sign the bill that would remove the required single admissions test, a key element of the city’s plan, Nixon repeatedly said, “I think it’s a start.” (A campaign spokeswoman, Lauren Hitt, later said that Nixon would sign it if it passed.)

The comments are the most specific Nixon has made about Mayor Bill de Blasio’s plan, announced this week in Chalkbeat, to increase diversity at the city’s top high schools, where collectively about 10 percent of current students are black or Hispanic and most students are Asian. The plan has won support from advocates who have long been pushing for changes but sparked fierce pushback from the schools’ alumni associations and some Asian-American community groups.

And while Nixon has long advocated for various education causes, she weighed in Thursday for the first time since launching her gubernatorial bid on the city’s broader school admissions policies.

Asked about schools that screen for admissions, which include schools that Nixon and at least one of her children attended, she said there’s more to be done to make sure schools are more racially representative of the city.

“We need to make sure that all students have access and that every school looks much more like a diversity of New York than it does right now,” she said, following a discussion with students about the school-to-prison pipeline.

But Nixon also implied that screening based on academic ability is typical of public school admissions. “Middle schools and high schools do that, generally speaking,” she said.

In fact, just 28 percent of schools citywide screen students based on grades, attendance, state test scores, and other factors, a system that contributes to extreme racial and academic segregation.

Nixon also weighed in on mayoral control of New York City’s schools, which requires approval of the state legislature. De Blasio has had to fight for that power repeatedly in Albany, and his control currently extends to June 2019, which means the debate will be live again this coming school year.

“I am tired of mayoral control coming up again and again and again. I think that it’s an issue that should be settled,” Nixon said.

Permanently? “I think so,” she responded.