For three hours this week, New York City Mayor Bill de Blasio and Edward D. Mullins of the Sergeants Benevolent Association held forth in secret at the Upper East Side home of one of the mayor’s top fund-raisers, feasting on deli sandwiches with cream sodas. The two discussed hurt feelings and bullet-resistant vests, a City Council bill about police chokeholds and the futility of the Knicks. When it was over, they exchanged cellphone numbers, pledging to keep in touch.

Nearly two months ago, the shooting deaths of two officers exacerbated a searing conflict between the mayor and the police, with an apparent work slowdown and explosive criticism from union officials stoking an intensely public rift. During that period Mullins called the mayor a "nincompoop."

The lurch toward reconciliation has come more quietly, aided by coincidences of timing, an evolving strategy from some union leaders and a series of well-placed nudges — both on and off camera — from Mr. de Blasio. And so, a sort of détente has set in, at least temporarily, the New York Times reports.

“We had an arranged marriage where the husband and the wife did not speak the same language,” Roy T. Richter, the president of the Captains Endowment Association, said of Mr. de Blasio’s relationship with officers at the time of his election. “It’s been a year filled with tragedies and disasters and horrible things, but I think that there is a dialogue now.”

In a series of interviews, police officials and union leaders described rank-and-file officers as at turns disillusioned with the protracted clash and increasingly mindful that Mr. de Blasio is, like it or not, their chief executive.

Then there were the vests. Though union leaders say the prospect of acquiring improved vests had been raised before at times, if never as a top priority, the issue came to the fore as part of an internal challenge to Patrick J. Lynch, the president of the Patrolmen’s Benevolent Association.

Union leaders say the recent policy announcements from the mayor and the Council owe to a newfound appreciation for the work officers do.

 “I think cops are appreciative of some of the steps the mayor has taken,” said Michael J. Palladino, the president of the Detectives’ Endowment Association. “But cops are suspicious by nature.”