New York City Mayor Bill de Blasio on Monday unveiled a $1 billion plan to provide free, full-day prekindergarten for all city 3-year-olds by 2021.

The mayor announced his plan at a South Bronx elementary school, saying the initiative would build upon the existing universal pre-K program for 4-year-olds that he pushed for at the start of his administration.

“The clock is ticking when it comes to the development of each young mind,” de Blasio said, citing studies that showed students who attended preschool for two years outperformed their peers who had not.

De Blasio said the city’s “3-K for All” plan would be funded by nearly $400 million in city money, and $700 million in state and federal funding the city plans to seek.

The plan will be implemented in phases starting with two low-income school districts in the South Bronx and Brooklyn’s Brownsville neighborhood this fall. By 2020, the city plans to expand the program to six additional school districts, and a year later the program would be available citywide in all 32 school districts.

The program is expected to serve about 62,000 children annually when fully implemented in 2021, according to the mayor’s office.

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De Blasio, a Democrat seeking re-election this year, acknowledged the pre-K expansion effort will “not be easy” — the city will need to find more classroom space, something it struggled with during the initial pre-K rollout, and will need to hire more teachers.

The plan must also win over state lawmakers in Albany — who have blocked a number of the mayor’s past legislative initiatives — and the GOP-led Congress, which has yet to approve the city’s $35 million reimbursement request for the cost of securing Trump Tower during the presidential transition.

“We believe based on the success in Albany last time we will be able to put together a coalition over the next two years to win funding,” de Blasio said, referring to the State Legislature and Gov. Andrew M. Cuomo signing off on a statewide universal pre-K funding plan in 2014 that helped the city launch its program.

The mayor said he has not yet reached out to the Trump administration regarding funding, noting that the federal contributions to the program would not be in play until “September of 2021,” after the 2020 presidential election.

“That’s a long way from now, and a lot can happen along the way,” de Blasio said, adding that early childhood education is “one of the areas that has seen more and more bipartisan interest.”