Physical education and the de Blasio administration’s school-turnaround program got a late boost in a budget deal announced Monday night by Mayor Bill de Blasio and City Council Speaker Melissa Mark-Viverito.

The $78.5 billion spending plan includes $6.6 million to hire physical education teachers and help the city fully comply with state regulations, and $17.9 million to phase in a program that will allow elementary school students to eat free breakfast in class. De Blasio’s “School Renewal” turnaround program will receive $15 million on top of what the city had already set aside in their proposal in May, money officials said would be directed at the extra hour of instruction each school will offer next year and to school health clinics.

The education add-ons, highlighted by the de Blasio administration in a press release, reflects some trade-offs between the city and the City Council. Both the school-food and physical education initiatives were driven by requests from Council members in recent weeks, while the city’s 94 struggling schools under the Renewal program have become a top priority for the administration.

The schools funding “signifies a true commitment to making schools that were often ignored the strong schools for all children,” de Blasio said Tuesday.

The deal directs $12.7 million to help pay for the extra hour of instruction each school in the Renewal program is set to offer next year. A May breakdown of the spending plan for the program from the Independent Budget Office noted that the city hadn’t indicated how much it would need to pay teachers and staff for that time, and the principals union also pushed back against the city’s plans for the extra time earlier this month.

That brings the city’s investment in Renewal Schools to $163 million for next year, a spokeswoman for the city’s budget office said. In the following year, the city plans to spend $183 million, including another $2.2 million for school-based health clinics.

The $6.6 million physical education initiative will go toward hiring 50 additional physical education teachers and to “conduct a comprehensive needs assessment to address barriers.” The City Council has been putting pressure on the city to show it was making efforts to comply with state laws after an audit last year found that many schools lacked certified teachers and students weren’t receiving the required amount of time in physical education class — a problem the city has faced for years.

The school-lunch initiative would introduce breakfast in the classroom at 530 elementary schools over the next two years, which officials said would serve 339,000 students by the 2017-18 school year.