Mayor Bill de Blasio has proposed an ambitious expansion of his popular prekindergarten program to all 3-year-old children in New York City.

The program, dubbed “3-K for All” by City Hall, will begin this fall as a pilot for about 2,000 children in District 7 in the South Bronx and District 23 in Ocean Hill/Brownsville, Brooklyn at a cost of $36 million. The city will spend another $177 million to expand the program to two more districts each year until it is operating in eight districts by the fall of 2020.

The mayor said he hopes to provide free, full-day preschool for all city 3-year-olds by 2021, but he said it would require an additional $700 million investment from the state and federal governments.

De Blasio said he will build on the success of his universal prekindergarten program for 4-year-olds, which has enrolled nearly 70,000 children. He estimated 4,500 more teachers would need to be hired.

Washington, D.C., is one of the few cities in the United States that currently offers free preschool to every 3-year-old. But while that program enrolls 5,700 students, the mayor’s proposal would eventually cover 62,000 children per year — making it one of the largest prekindergarten programs in the country.

Research shows early childhood education pays dividends down the road. “The early years of life are critical for developing the architecture of the brain and future capacities to learn,” said Professor Beverly Falk, the director of Graduate Programs in Early Childhood Education at the City University of New York.

Falk cited a longitudinal research study following children over 40 years that found “children from poverty who had high-quality care as 3- and 4-year-olds were more likely to do better on a range of measures as adults,” including high school graduation, home ownership and future earnings.

Falk estimated the return on investing in early childhood education is about $13 for every dollar spent.