At the same time the de Blasio administration has been rapidly growing the city’s free pre-kindergarten program, it has also been urging parents to get more involved in the school system.

But there’s a catch: One of the few formal roles that parents can play in the system is to join a local education council, but those councils are not open to pre-K parents.

Now, some politicians are calling for an amendment to state law that would let those parents run for spots on the councils, which officials see as a key way to get parents to play an active part in the school system as soon as they enter it.

“If we have an involved and engaged parent at an early level,” said Brooklyn Borough President Eric Adams, who requested the rule change, “it turns into an involved and engaged parent throughout the process, and the entire system benefits because of that.”

Adams said the amendment could encourage more parents to run for spots on the community education councils, which are currently only open to parents of students in kindergarten to eighth grade. (There is a separate citywide council for high school parents.) While the city boosted the number of candidates this year, only a tiny fraction of eligible parents apply to run and certain councils attract far more applicants than others.

Each of the city’s 32 school districts has a CEC with a dozen volunteer members, including nine parents who are voted on by the district’s parent-association leaders. (This year’s voting process begins Sunday.) The council members, who serve two-year terms, approve school zones, hold hearings on district spending plans, and give recommendations on certain policies.

Some current council members on Monday welcomed the effort to involve more parents at an earlier stage. But they also raised several questions about the proposal: Would parents at public pre-K programs run by charter schools or community-based organizations be eligible for council seats? And would pre-K parents compete for a school’s single council spot, even though they may switch to another school the following year?

“It’s nice to be inclusive and try to get pre-K parents to join earlier,” said Laurie Windsor, president of the CEC in Brooklyn’s District 20. But, she added, “I don’t understand how that’s going to work.”

Having campaigned on the need for greater parent input on school-policy decisions, Mayor Bill de Blasio made a strong push to recruit more candidates for this year’s CEC elections. The city ran subway ads in nine languages, held dozens of information sessions, and made thousands of robocalls to parents. As a result, 1,290 parents applied for spots on the local and citywide councils, a 77 percent increase over the previous election.

Still, certain districts saw more action than others. For instance, more than 35 parents applied for the nine council seats in some Brooklyn districts, while just a dozen or so applied for those spots in other parts of the borough, according to Adams’ office.

Adams said that opening up the elections to pre-K parents and urging them to apply could draw more parents into those less competitive council races. But Windsor and other council members questioned how many pre-K parents want or are qualified to weigh in on district-wide policies if they are still new to the system and its complexities.

They raised other concerns too. Council seats are currently only open to parents of district-school children, but more than half of public pre-K seats are provided by community-based groups (six charter schools also participate in the program). Also, some parents send their children to pre-K sites outside of the school zones where they live. Since state rules only permit one council member from any single school in the district, a pre-K parent could potentially snag a school’s council seat before moving to a different school the next year.

“That’s not fair to the person who really is zoned to that school,” Windsor said.

Officials in Adams office said that if parents change schools they would still be expected to complete their two-year terms. They added that the amendment limits eligibility to district-school parents, but that legislators could debate opening up seats to parents in community-based and charter school pre-K programs.

State lawmakers recently introduced the amendment, which is now being considered by the senate and assembly education committees. If adopted, it would apply in the 2017 elections.