Some of those impressed by the depth of Mr. Bloomberg’s feelings have been struck in part because he had disappointed many when, by their lights, he failed to stand behind the principal of the city’s first Arabic-language public school.

The case of the principal, Debbie Almontaser, began, much as the community center did, with a seemingly uncontroversial plan  a school that would teach Arabic. Soon enough, though, conservative advocates, inflamed by the proposal, branded Ms. Almontaser a “radical” and “jihadist.”

After opponents sought to link her to T-shirts that said “Intifada NYC” and a newspaper suggested she had defended the slogan, the Bloomberg administration forced her to resign in 2007, she said.

A federal employment commission determined that Ms. Almontaser had not been connected to the T-shirts, that the newspaper had misconstrued her words and that the Bloomberg administration “had succumbed to the very bias that creation of the school was intended to dispel.” (The school has survived and is run by a new principal.)

Now, some Muslim leaders in New York express pleasant surprise at his position on the downtown center.

Robina Niaz, executive director of the Muslim social service group Turning Point for Women and Families, said his position in the Almontaser case “was totally the opposite, completely the reverse of this.”

Her sense, she added, was that Mr. Bloomberg “may have gone back and looked at how that was not helpful as a mayor, as a leader  that this was an opportunity to undo some of that.”