New York City officials on Tuesday announced which school districts are next in line for free pre-K for 3-year-olds, identifying East Harlem and the eastern neighborhoods of Queens for expansion of the program.

Building on its popular universal pre-K program for 4-year-olds, the city this year began serving even younger students with “3-K For All” in two high-needs school districts. Mayor Bill de Blasio has said he wants to make 3-K available to every family who wants it by 2021.

“Our education system all over the country had it backwards for too long,” de Blasio said at a press conference. “We are recognizing we have to reach kids younger and more deeply if we’re going to be able to give them the foundation they need.”

But making preschool available to all of the city’s 3-year-olds will require an infusion of $700 million from the state or federal governments. In the meantime, de Blasio said the city can afford to expand to eight districts, at a cost of $180 million of city money a year.

Funding isn’t the only obstacle the city faces to make 3-K available universally. De Blasio warned that finding the room for an estimated 60,000 students will be a challenge. Space constraints were a major factor in picking the next districts for expansion, he said.

“I have to tell you, this will take a lot of work,” he said, calling it “even harder” than the breakneck rollout of pre-K for all 4-year-olds. “We’re building something brand new.”

De Blasio, a Democrat who is running for re-election in November, has made expansion of early childhood education a cornerstone of his administration. The city kicked off its efforts this September in District 7 in the South Bronx, and District 23 in Brownsville, Brooklyn. More than 2,000 families applied for those seats, and 84 percent of those living in the pilot districts got an offer for enrollment, according to city figures.

According to the timeline released Thursday, the rollout will continue next school year in District 4 in Manhattan, which includes East Harlem; and District 27 in Queens, which includes Broad Channel, Howard Beach, Ozone Park and Rockaways.

By the 2019 – 2020 school year, the city plans to launch 3-K in the Bronx’s District 9, which includes the Grand Concourse, Highbridge and Morrisania neighborhoods; and District 31, which spans all of Staten Island.

The 2020 – 2021 school year would see the addition of District 19 in Brooklyn, which includes East New York; and District 29 in Queens, which includes Cambria Heights, Hollis, Laurelton, Queens Village, Springfield Gardens and St. Albans.

With all those districts up and running, the city expects to serve 15,000 students.

Admission to the city’s pre-K programs is determined by lottery. Families don’t have to live in the district where 3-K is being offered to apply for a seat, though preference will be given to students who do. With every expansion, the city expects it will take two years for each district to have enough seats for every district family who wants one.