Some parents were distraught, fearing that bright students would be left bored and restless at their desks.

Others questioned whether teachers can truly determine whether a 4-year-old is gifted.

And rival candidates in the mayor’s race pounced.

The divided reactions across New York came after Zohran Mamdani, the Democratic front-runner for mayor, said this week that he planned to end the city’s gifted and talented program for kindergarten students at public schools if he is elected. Students who are already in gifted classes would remain in the program, and his campaign said on Thursday that he would keep a separate track next year that admits students in third grade.

New York’s program stands apart from many other major cities that admit children into gifted classes starting in later grades. It is small: New York’s school system enrolls about 2,500 students out of 55,000 kindergartners.

Children are selected during pre-K by their teachers; a previous system that tested 4-year-olds was abandoned four years ago.

But it can play an outsize role in directing students’ educational paths and regularly emerges as among the most provocative education issues in the nation’s largest school system.

The highly selective program is often viewed as a steppingstone to the city’s competitive middle and high schools. Many families clamor for access to gifted classes as a way of ensuring that high-achieving children can be challenged and receive prime educational opportunities in later grades.

But critics say the gifted program exacerbates inequality in a school system deeply divided along lines of race and income. Black and Latino students are enrolled in gifted classes at far lower levels than their overall presence in the public school system.

The competing realities have ignited years of contention among parents and politicians about the future of gifted education in New York, including four years ago when Bill Bill de Blasio announced a plan at the tail end of his term as mayor to phase out the program.

On Thursday, the school system barreled toward a resurgence of this complicated debate. Hours after Mr. Mamdani’s plan became public, his opponents in the mayor’s race attacked his vision for the program and the school system.

Former Gov. Andrew M. Cuomo, a Democrat who is running as a third-party candidate, wants to expand gifted classes. He blasted Mr. Mamdani’s proposal as “destructive and emblematic of a deeper problem in today’s Democratic Party — the surface level appearance of a solution is sufficient.”

This year, about 10,000 families applied for the kindergarten gifted program, which Mr. Cuomo said shows that parents “want more of it, not less.”

“That program is the one program that allows extraordinary students to actually excel,” Mr. Cuomo said at a news conference on Thursday. “You take away gifted and talented programs, the one possibility that your child might get a really first-class education in public schools goes with it.”

Mr. Mamdani had shared his plan in response to a questionnaire that The New York Times sent to the leading candidates in the race about challenges the city is facing.

Dora Pekec, a spokeswoman for the Mamdani campaign, said in a statement that Mr. Mamdani’s agenda would ensure that all students receive “a high-quality early education that enables them to be challenged and fulfilled.”

“Zohran knows that 5-year-olds should not be subjected to a singular assessment that unfairly separates them right at the beginning of their public school education,” she added.

While the families of public school students in the city may be dissatisfied with the state of gifted education, they share little agreement about solutions.

The issue does not always break cleanly along political or racial lines. Some Asian families question the value of a separate program and ask whether preschools are failing to identify all gifted children, and some Black and Latino parents have called for expanding the program in sections of the city with limited access.

In District 2, one of the wealthiest sections of the school system that includes the Upper East Side, the West Village and TriBeCa, about 1,120 families applied and roughly 350 students received seats in the gifted program this year. In District 4, which covers East Harlem, 97 applied and 16 received seats.

As candidates waded into an education issue that is often considered a third rail, many WhatsApp group chats of public school parents lit up on Thursday.

“This is just a hornet’s nest to step into,” said Yiatin Chu, a public school parent and the co-founder of Parent Leaders for Accelerated Curriculum and Education, a group that has advocated for gifted and talented programs.

She said that Mr. Mamdani’s plan could take a particular toll on families who can’t pay for private education or for additional academic opportunities to supplement the school day.

“It’s hurting the people that he talks about helping: the working class and the middle class,” she said, adding that the school system could not treat students like “one size fits all.”

Nyah Berg, the executive director of New York Appleseed, an advocacy group pushing for integrated schools, said that factors beyond a child’s intelligence appear to weigh in admission into kindergarten gifted programs.

She added that many families view the program as a means of “mobility to be able to have the best quality education possible for your child.”

“Really, people are looking for accelerated learning opportunities that are widely accessible — and that’s just not the case with the way we have gifted and talented,” Ms. Berg said.

In an election in which affordability, housing and public safety are the dominant issues, it remains unclear whether a candidate’s stance on the gifted program — or any education issue — will sway large numbers of voters.

Still, Curtis Sliwa, the Republican nominee, took the plan as an opportunity to launch a broadside against both Mr. Mamdani and Mr. Cuomo, calling them “two peas in a pod.”

He said that when the de Blasio administration pursued changes to admissions in the selective academic programs, Mr. Cuomo “either backed parts of it or stayed silent” — and that Mr. Mamdani was now “pushing the same agenda.”

“We are not letting Mamdani and his mentor Cuomo fail our children again,” Mr. Sliwa wrote on social media.

(Mr. Cuomo has said that he would expand a group of selective high schools if elected, and Rich Azzopardi, a spokesman for the former governor, called Mr. Sliwa’s comments inaccurate.)

Matt Gonzales, a former member of a school diversity advisory panel under Mr. de Blasio, said he hopes that if Mr. Mamdani is elected, his gifted and talented plan would reflect a broader effort to create a more inclusive and equitable school system.

“It’ll be controversial,” Mr. Gonzales said, while adding, “it’s the right way to go.”

Jeffery C. Mays contributed reporting.