After the vote, Mr. Koppell said the existing schedule of religious holidays might have to be reviewed and trimmed, lest other growing religions in New York start demanding their own days off. “Where are we going to end with this?” he asked.

The resolution’s advocates said that since about 12 percent, or more than 100,000, of the city’s public school students are Muslim, they deserved recognition. The two holidays have already been adopted by school districts including Dearborn, Mich., and several municipalities in New Jersey.

Supporters also say that since the Ids (pronounced eeds) are floating holidays whose timing is set by the lunar calendar, they often fall on other religious holidays, on weekends or during the summer. During the next decade, for instance, at least one of the two Ids each year is expected to coincide with summer recess or an existing school holiday, according to a report by the Immigrant Rights Clinic at New York University.

It was unclear on Tuesday whether Mr. Bloomberg would continue to have final say on the issue, because the State Legislature still has not passed a bill to extend his control over the schools. But some officials said that even if the bill did not pass, he would be able to exert indirect control through appointments to the Board of Education.

The Council resolution also urged the Legislature to pass two pending bills that would amend state education law to require the holidays in the city’s school calendar. That could allow the move without the mayor’s approval, said Councilman Robert Jackson of Manhattan, a co-sponsor of the resolution and a Muslim.

Id al-Fitr celebrates the end of Ramadan, the sacred month of fasting, and Id al-Adha, the Festival of Sacrifice, marks the end of the annual pilgrimage to Mecca. Muslims traditionally observe these days by praying in the morning, then celebrating with family and friends, exchanging gifts and sharing a large meal.

The holy days have long posed a painful choice for Muslim students: Should they go to class in the interest of their grades and attendance record, or cut class to be with their families?