NEW YORK » Not long after Mayor Bill de Blasio sat beside the Rev. Al Sharpton at a July summit meeting on police reform, a political adviser gave the mayor a blunt assessment: You have a problem with the cops.

Rank-and-file officers felt disrespected by the mayor, the adviser explained, and were dismayed to see Sharpton, a longtime critic of the New York Police Department, embraced at City Hall.

But de Blasio, a Democrat, rejected the notion that officers disliked him. His message, the adviser later recalled, was clear: Everything was under control.

That confidence would last until late last month, when the murders of two officers in Brooklyn prompted the department to adopt a stance of rebellion. Uniformed officers protested against the mayor in public, and low-level arrests virtually stopped. De Blasio, a liberal who had staked his mayoralty on re-educating the police force, is struggling to secure its basic trust.

In recent days, de Blasio has sounded downcast, according to aides who have spoken with him. The manager of his mayoral campaign has returned to help. And his team is considering focus groups and a poll to refine the mayor’s message to New Yorkers who may have soured on him.

How de Blasio reached this point is a story of accumulated slights, political miscalculations and the slowness of members of his inner circle, almost none of whom have close ties to law enforcement, in reacting to the warning signs of what would become the gravest crisis of his young mayoralty.

It is also a story of a Police Department that has proved vexing for mayors to manage in recent years, and whose members have grown increasingly frustrated with their leaders and critics alike.

Eager to show respect for police officers, the mayor instead unwittingly antagonized them, committing gaffes whose consequences his team was slow to grasp.

Inside City Hall, the mayor had not anticipated how police officers might react when he hired Sharpton’s former spokeswoman, Rachel Noerdlinger, as a top aide, despite his team’s knowing her live-in boyfriend was a convicted killer.

And even as police unions assailed the mayor, de Blasio’s advisers remained convinced that the demographics of the rank and file were changing in his favor. The Police Department, aides argued, was morphing into a multicultural force whose members increasingly shared the views of the diverse group of voters who elected him in a landslide in 2013.

In interviews, exasperated mayoral aides said that de Blasio has time and again voiced support for the police, even defying key supporters by endorsing the aggressive "broken windows" strategy that some liberals want to end. They blame police unions for instigating hostilities amid contract talks. And they argue that the department is bristling against a reform-minded mayor unafraid to broach difficult questions of policing and race.

Still, in dozens of interviews in recent weeks, patrol officers and senior police leadership alike described a sense that the mayor did not stand behind them, or appreciate the difficulties of their work. Many said a rift had opened up between de Blasio and the Police Department that would not easily heal.

Notably, while some officers have been emboldened to express themselves openly in groups and through public demonstrations, those interviewed were unwilling to break departmental rules and risk punishment by speaking freely for this article.

"You can’t just say, ‘Look, I’m saying I support you, so change the way you feel,’" one police officer said. Invoking a failed marriage, he added: "Even if you go through the motions of trying to reconcile, the feeling isn’t there."

As a candidate for mayor of New York, de Blasio, who declined through a spokesman to comment for this article, tapped into a widespread dissatisfaction with the Police Department, particularly in black and Hispanic communities. He denounced the use of the stop-and-frisk tactics, endorsed an independent monitor and marched alongside liberal advocates who said the police unfairly targeted minorities.

And yet, as he took the oath of office last January, a sense of cautious optimism had emerged in precinct station houses and at 1 Police Plaza.

One reason was William J. Bratton, a towering figure in law enforcement and de Blasio’s pick for commissioner. No one’s idea of someone who was soft on crime, Bratton was a reassuring and even an exciting choice to officers who viewed him as a sign that the mayor cared about their work.

The rollback of the stop-and-frisk policy, by then already underway, was not unwelcome, either: Officers had long bemoaned orders to make a certain number of stops each month, saying it stripped them of discretion.

De Blasio, aides said, saw Bratton as a potent emissary to a law-enforcement world the mayor knew little about. With Bratton handling law and order, de Blasio believed, he could focus on his fight against inequality, an aide recalled.

But as time went on, officers’ worries began to take hold.

Some bristled when Noerdlinger, the former Sharpton aide, was named chief of staff to the mayor’s wife, Chirlane McCray. And when a television reporter caught the mayor’s city-issued SUV speeding, other officers noticed, de Blasio failed to take responsibility, implicitly faulting his police detail.

And in November, when de Blasio arrived late to a memorial ceremony in in Queens, his aides said his police boat had been delayed by fog. The mayor later conceded he had overslept. The incidents left an impression that the mayor could undermine the police, an impression that was repeatedly reinforced.

The unease that had been simmering first boiled over in July, after Eric Garner, an unarmed black Staten Island man, died after being placed in a police chokehold.

Eager to address the furor, de Blasio invited journalists to attend a roundtable discussion at City Hall, intended as the sort of "come together" moment that he prides himself on.

But the stagecraft was odd from the start. On the mayor’s right sat Bratton; on his left was Sharpton, the symmetry suggesting the two held equal sway in the administration. When Sharpton began a broadside on law enforcement, the mayor silently looked on.

"That just blew our minds," said one supervisor, recalling the reaction of officers in his precinct. "He completely wronged the cops on that one." The cover of The New York Post screamed a question: "Who’s the Boss!"

Publicly, the mayor defended the talk. Privately, City Hall knew it had erred. At a meeting with high-level aides in the ornate Committee of the Whole room, de Blasio urged them to better anticipate how events might be perceived.

The Sharpton episode could have been a turning point. But City Hall’s approach did not change.

In private conversations, de Blasio and his aides expressed confidence that they had handled things well. Internal Police Department surveys, they said, showed that officers were more focused on internal matters, like disciplinary policies that predated his administration. The mayor told aides that police officers had the same concerns as other working-class New Yorkers, the group he was determined to champion.

And, City Hall reasoned, the mayor had amply demonstrated support. His administration added more than $350 million to the Police Department budget, improving facilities and giving thousands of digital tablets to officers. De Blasio staunchly defended the "broken windows" policy of pursuing small crimes to deter bigger ones, even as his liberal base seethed that Garner, who officers said had been selling illegal cigarettes, was a casualty of that policy.

For many officers, however, such gestures of goodwill were being overshadowed. And de Blasio, unlike previous mayors, had few advisers with experience managing a political relationship with the Police Department, apart from Bratton himself.

Indeed, aside from Cardinal Timothy M. Dolan, the archbishop of New York, the administration had few avenues for outreach to the blue-collar, white New Yorkers who make up much of the department – and most of its union leadership – but who are not among de Blasio’s core political supporters.

When it emerged in September that Noerdlinger’s son and boyfriend had written virulently anti-police messages on social media, and that her boyfriend had nearly run over a New Jersey state trooper while driving her car, de Blasio spent weeks defending her, even after investigators found that she had failed to mention her boyfriend on a city background questionnaire.

The mayor’s team was incensed, seeing racial motivations in attacks aimed at Noerdlinger, a black woman with close ties to Sharpton.

The reaction of the rank and file was not a major factor in de Blasio’s thinking, a person briefed on internal discussions said.

By early December, Noerdlinger had stepped down, and the death of Michael Brown, a black teenager in Ferguson, Missouri, had prompted a national uproar over.

When a Staten Island grand jury decided not to indict the officer in the Garner case, de Blasio pursued what his team believed was a responsible, middle-of-the-road position.

Aware that anti-police demonstrations could ensue, the mayor said it was not his place to criticize the grand jury’s decision. (Other prominent Democrats, including U.S. Sen. Kirsten E. Gillibrand of New York, did.)

In an impassioned speech, de Blasio said that he and his wife, who is black, had to instruct their son, Dante, about the "dangers he may face" in an encounter with the police. The mayor had no prepared text, and some of what he said was off-the-cuff; aides refused to say if he had planned to speak about his son.

The comments were welcomed by large swaths of New Yorkers, who recognized a difficult conversation that they, too, had had with their children.

But police union leaders took his remarks as an insult that betrayed his true feelings.

And in interviews, even officers who sympathized with the mayor’s point said he had picked an inopportune moment to make it.

"The NYPD is incredibly diverse, and our cops don’t carry around some sort of historical baggage when they go out there and try to make minority communities safe," said one officer, who is white. "It wasn’t the right thing to say to the world as a message of calm and mutual respect after the Garner decision."

Later, de Blasio said he had not intended any disrespect. "It was an attempt to open up a real discussion of what is going on here and what has been going on for generations so that we can move forward," he said in a Dec. 19 interview.

"You can’t heal a sickness if you don’t acknowledge it," he added.

As protests over the Garner case broke out in New York City, top police officials, with the blessing of the mayor, allowed demonstrators to temporarily take over streets and highways, puzzling many officers and commanders in the field who were accustomed to a tougher approach.

When two officers were assaulted by protesters, de Blasio quickly issued a statement denouncing the attack. But Ed Mullins, president of the Sergeants Benevolent Association, objected to the mayor’s use of the word "allegedly" to describe the assault.

The mayor’s team found the charge absurd. But they also believed that a tense period was coming to an end. Days after the Garner decision, the administration announced a contract agreement with unions representing police detectives and supervisors.

In the Dec. 19 interview, the mayor said the Police Department was "in evolution."

"There’s a lot more work to do in terms of helping our officers to feel good about the work they do," the mayor said. But he also expressed optimism, saying, "There’s going to be a feeling, sort of a calming dynamic as people settle into a new approach."

The next day, two officers, Wenjian Liu and Rafael Ramos, were fatally shot in Brooklyn while sitting in their patrol car. The assailant, a mentally ill man from Baltimore, had pledged on his Instagram page to put "wings on pigs."

The raw fury from union leaders after the shootings caught City Hall by surprise.

Patrick J. Lynch, president of the 24,000-member Patrolmen’s Benevolent Association, said there was "blood on the hands" of the mayor, and prompted officers to turn their back on the mayor as he entered a hospital to console the slain officers’ families.

For de Blasio, who thought he had managed to find a middle ground, it was a deeply painful moment. Some aides who spoke to him in the days afterward described him as sounding depressed.

Little happened in the following days to lift his mood.

Members of the Police Department turned their backs on him again at the slain officers’ funerals. He was booed at a graduation ceremony. Weekly statistics showed officers cutting back on low-level arrests and the issuing of summonses. Last week, a flier with a photo of his wife was passed around police circles, accusing her of inappropriately wearing bluejeans to one of the funerals; mayoral aides clarified that the outfit was a designer pantsuit.

The mayor is now shifting his approach. He took pains last week to emphatically convey respect for the police, trumpeting current low crime rates while twice describing the force as "the world’s greatest."

He also criticized the back-turning protests, echoing mayoral aides who were privately furious over the incendiary remarks of police union leaders.

"This is a mayor who – not for show, not for cameras, not just in the past six weeks – when passing a cop on the beat, or a cop standing post, shakes hands and engages," said Phil Walzak, the mayor’s press secretary. "A meet-and-greet, and words of thank you, to virtually every cop he comes across in the city doing their job."

Bratton, meanwhile, appears to have achieved the middle ground de Blasio so keenly sought, requesting, not ordering, officers not to turn their backs on the mayor, and criticizing, but not punishing, those who protested. He retains officers’ loyalty, even while standing closely by the mayor.

For now, City Hall is mulling its options, with advisers holding strategy sessions at the offices of an outside political consultant.

De Blasio’s team does not believe he should apologize, saying it would suggest the Police Department had too much sway over the administration. His advisers believe public opinion could soon turn their way, noting that many New Yorkers were dismayed at the funeral protests and police slowdown, and were glad to see the mayor urging calm.

Aides also signaled they would like to settle outstanding contracts. "If anyone in our workforce feels they got the shaft from past mayors or governors, we are certainly committed to addressing their real issues," Peter Ragone, a senior adviser to de Blasio, said.

One police detective, a native New Yorker, dismissed Lynch’s attacks as "ridiculous" and said de Blasio was not solely at fault.

But the detective, 39, who is white, said de Blasio would face problems as long as his approach made him an easy scapegoat for what many officers perceived to be an unfair national backlash against police.

"He is the most visible target for people’s anger," said the detective, a registered Democrat, adding, "I don’t think de Blasio hates the police. But I don’t know if he can mend the fence."

Michael M. Grynbaum, J. David Goodman, and Al Baker, New York Times

© 2015 The New York Times Company