Nine private programs that were to offer free, city-financed prekindergarten this year will not open because of safety concerns or other issues, and 36 programs will not be ready to open on Thursday, the first day of school, New York City officials announced on Tuesday.

Extending free, full-day prekindergarten to all 4-year-olds was Mayor Bill de Blasio’s signature campaign proposal and for him, much is riding on the program’s success. The 45 programs cited on Tuesday by the city represent a small percentage of the roughly 1,100 private sites that are scheduled to open on Thursday.

Over 50,000 children have been signed up for full-day prekindergarten programs this year, an increase of 30,000 from last year. The city plans to add 20,000 more seats next year.

About two-thirds of the seats are in private programs, which have undergone rigorous inspections by fire and health officials and employees of the Education Department. The city had said that if sites still had serious health violations or other problems by now, they would not open, but Tuesday was the first time that the city said that some programs would not open at all.