Expanding pre-kindergarten will be more expensive than expected, Mayor Bill de Blasio said Thursday as he revealed a spending plan that includes additional funding for pre-K and the city’s school-turnaround program.

The 2016 budget includes $409 million for the city’s growing pre-K program, which is expected to enroll more than 70,000 four-year-olds next year. The city had estimated the cost at $340 million in February, a figure de Blasio said had grown because of increased demand and the steep cost of finding private space for pre-K classrooms in areas where the public schools had none to spare.

“It’s more popular than even we knew it would be, so we’re hitting the high end of our numbers,” de Blasio said. “We know the costs are going to be higher than anticipated, but it’s absolutely worth it.”

Nearly 69,000 families applied for a pre-K seat last month, according to the city. The borough with the biggest increase in applications was Queens, where many neighborhoods have perennially overcrowded schools.

“The physical build-out is proving to be a challenge in the sense that we have to find a lot more space in a number of neighborhoods where there’s school overcrowding, so we didn’t have the option to go into our existing schools and find additional space,” de Blasio said.

The city is also set to spend $108.3 million on the “Renewal” turnaround program next fiscal year, up from $30.7 million this fiscal year, officials said, a sign that the program will shift toward more intensive support and student services next year. Last fall, de Blasio promised to invest $150 million in 94 low-performing schools over three years to pay for extra services for students and training for staffers.

Officials added that the education department had repurposed more than $40 million in federal funds to use for struggling schools. That is in addition to another $34 million being allocated to boost the budgets of those schools, and other schools with low attendance that are getting extra services in order to become “community schools.”

Struggling schools will also receive funding to offer more academic help to overage eighth graders, vision screenings for students, additional science programs, and access to a substance abuse prevention specialist, according to budget documents, and 63 new guidance counselors will head to “high-needs” schools.

“We are going to just keep adding elements to turn these schools around,” de Blasio said.

The city isn’t allocating extra money for its after-school programs, which it also expanded to all middle schools last year. In February, the city said it would spend $190 million to serve 100,000 students; on Thursday, it said it would only spend $163 million but serve 107,000 students.

The city will allocate funding for 444 new programs in the Public School Athletic League, a significant increase. The city has faced ongoing criticism for the options available to students at small schools, prompting some recent student protests.

Meanwhile, the results of an experiment offering free lunch to middle-schoolers this year haven’t been convincing enough to expand it to other grades, de Blasio said. Middle schools will offer free lunch again next year to allow for a “more thorough test.”

“The results are mixed so far in terms of the impact it’s having, meaning the additional number of children who are taking advantage of it,” de Blasio said. “It’s not been that large so far.”

City Council members and Speaker Melissa Mark-Viverito have called for extending the program to all students, as have advocates, who say the pilot program was effective. In March, Fariña told the City Council that there was a 6.4 percent increase in the share of students eating free lunch at the 291 middle schools that were part of the program.

“Universal free school lunch in middle schools this year is proving to be an amazing and well-documented success. It is a no-brainer to ensure that all 1.1 million students are included in the June final budget,” said Liz Accles, executive director of Community Food Advocates.

Overall, the education department’s operating budget for 2016 stands at $21.7 billion, which includes $533 million more from the state than the city received last year.

The City Council will hold hearings on the budget before a final version is adopted in June. An education committee’s hearing is scheduled for May 28, and the new fiscal year starts July 1.