In fact, it was a secular group, the political organizing arm of Local 32BJ of the Service Employees International Union, which represents school cafeteria workers, bus drivers and maintenance workers, that in 2006 began coordinating the formal campaign to close the schools for the Muslim holidays, after the state incurred anger by scheduling a Regents exam on Eid al-Adha. Since then, the Coalition for Muslim School Holidays has brought together dozens of Muslim and non-Muslim clergy and community leaders and won the endorsement of the United Federation of Teachers and other labor and civil rights groups.

Organizers stress that granting the Muslim holidays equal status with Jewish holidays like Yom Kippur and Christian holidays like Christmas would send a powerful message to Muslim children — who often seek to blend in more than stand out — that they can be proud of their own culture.

Debbie Almontaser, who was forced out of her job as principal of the city’s first Arabic language school, in Brooklyn, in 2007 after The New York Post inaccurately portrayed her as sympathizing with Muslim extremists, now works at the Benjamin Banneker Academy, another public high school in Brooklyn. She sees many of her Muslim students grappling with how to express their identity.

“There is so much negativity out there, and including the Muslim holidays is simply a stamp of saying, We accept and embrace you, and this is your city as it is my city,” she said.

The coalition won its first big victory in 2009, when it got the City Council to overwhelmingly pass a resolution to grant the days off. But Mayor Michael R. Bloomberg would not implement the idea, saying children needed more time in school, not less.

In the years since, the Muslim community has grown more organized politically. In 2013, for example, the Arab American Association of New York and the Islamic Center at New York University sponsored a debate among the mayoral candidates. In answer to a child’s question, all of the candidates present, including Mr. de Blasio, pledged to close the schools for the Muslim holidays; the Republican candidate, Joseph J. Lhota, later followed suit. The moment was freighted with emotion for many Muslims.