“I am so appreciative for what you do to represent the Italian-American community. . . . This is what our great-grandparents, our grandparents dreamed of,” he said.

But his attempt at building bridges wasn’t all that successful.

When he asked who agreed with him that the NYPD was the “finest police force anywhere,” he was met with only halfhearted hurrahs — no one stood up, whooped or hollered in agreement.

The biggest applause came when de Blasio singled out Office of Emergency Management Commissioner Joseph Esposito, a former NYPD chief of department.

In contrast, the crowd clapped only minimally for Police Commissioner Bill Bratton when de Blasio called out his name.

The enthusiasm for Esposito wasn’t lost on de Blasio.

It is not unusual for mayors to want irritating story lines to go away. But the Noerdlinger episode has fueled a broader question about Mr. de Blasio and the values of his young administration: how a onetime champion of transparency and accountability can square those ideals with the newfound power — and frustrations — of his office.

As a candidate, Mr. de Blasio pledged an ask-me-anything era at City Hall, promoting himself as a different, friendlier breed of political leader. And as public advocate, he frequently assailed former Mayor Michael R. Bloomberg for standing by senior aides, such as the former schools chief Cathleen P. Black, who had found themselves under fire.

And it hit inboxes on the same morning that thousands of charter school supporters held a rally, promoted by Eva S. Moskowitz — an antagonist of Mr. de Blasio’s who has acknowledged thinking about running for mayor in 2017 herself.

[. . .]

When contacted about their relationship and McFarlan’s comments, the mayor’s office backed Noerdlinger as a key aide to the administration, but said it did not tolerate derogatory comments about police.