NEW YORK (CBSNewYork) – While discussing record low crime in New York City, Mayor Bill de Blasio praised the work of the NYPD and its commissioner — while tensions between the mayor and police unions continue to simmer.

But the mayor and Commissioner Bill Bratton both took issue with officers who have turned their backs on the mayor in public, and otherwise castigated him as being unsupportive.

De Blasio, speaking at 1 Police Plaza, took reporters’ questions Monday for the first time in about two weeks.

The mayor said the overall crime rate dropped 4.6 percent in 2014, and that NYC had the lowest number of murders since 1993.

The mayor spent several minutes touting the achievements of the police department, while also acknowledging recent tensions with police unions.

“There’s a lot to be done, but we have momentum,” de Blasio said. The mayor also said, “the people of this city appreciate the police. They see how hard the work is.”

De Blasio and Bratton also discussed some specific police policies that have come under fire.

Some activists have called for an end to the broken windows policing strategy – the theory that enforcing quality-of-life laws will serve to prevent more serious crimes. The calls to end the policy have increased in particular since the death in police custody of Eric Garner, who was put in an apparent chokehold as police tried to arrest him for allegedly selling loose cigarettes.

But Bratton and Mayor de Blasio both defended the policy, and emphasized how some New Yorkers may not realize how severe the problem once was. In 1990, the city recorded a total of 2,245 murders.

“Half the people living in the city now were not here in 1990, and have no understanding of how bad it was,” Bratton said.

He called the Garner incident an “aberration” in the use of the broken windows policy, and not a reason to abandon it.

De Blasio also said many people do not realize how dire the situation in the city once was.

“This is breathtaking, the information that we have here. Those of us who were here in the 1980s and 1990s could never have imagined these kind of numbers,” de Blasio said. “They are the result of a proactive strategy, and the result of a number of strategies — one of which is the broken windows approach.”

But de Blasio said police have, in fact, cut down on practices that left some communities feeling stigmatized and targeted. In particular, he pointed to the decision by the NYPD to begin issuing tickets for low-level marijuana offenses.

The policy change on marijuana began in late November.

Marijuana arrests are down 50 percent over the last three years, and 10 percent in November and December 2014, he said. The mayor argued that the change in policy has improved relations between communities and police officers, since people’s “children or nieces or grandchildren” no longer have to fear being saddled with a criminal record.

De Blasio also pointed to changes made to the stop-and-frisk policy, and said despite criticism, many police officers also thought the decisions on the policy were for the best.

“We made a serious of chances that in fact were better or our officers and our communities alike…. Some of the police unions themselves believe that the stop-and-frisk policies of the previous administration were creating tension between officers and the communities they served,” de Blasio said.

Hundreds of police officers turned their backs to the mayor during the funerals of officers Wenjian Liu and Rafael Ramos — who were gunned down in Brooklyn while sitting in their patrol car on Dec. 20.

“It is the world’s greatest police department because it is constantly committed to getting better,” de Blasio said. “We’re going to find a way forward together, that I remain convinced of.”

But he called the officers who turned their backs “disrespectful to the families involved… and I can’t understand why anyone would do such a thing in a context such as that.”

Bratton had issued a memo asking officers not to turn their backs on the mayor at Liu’s funeral in a memo that was read at all roll calls prior to the funeral. He said he shared de Blasio’s concerns about the officers taking what he called a “labor action” in the middle of a funeral.

“I just don’t understand it. I’m sorry, but I just do not understand it,” Bratton said. “What was the need in the middle of that ceremony to engage in a political action? I don’t get it. And I’m very disappointed for those who did not comply with my request.”

He called the back-turning action “selfish” and said the officers who did it “embarrassed themselves.”

“You don’t put on a uniform and go to a funeral and perform a political act,” he said.

Bratton also emphasized that the Police Department has many issues going on which are fanning the flames of dissatisfaction, and which the de Blasio administration is trying to solve. Among them are contracts that Mayor Michael Bloomberg’s administration that de Blasio is working to settle, and various retirement plans, Bratton said.

Bratton also addressed claims that police officers have coordinated a work slowdown as part of a continuing rift between the police force and the mayor. In the week since the deaths of officers Ramos and Liu, the numbers of arrests in some areas dropped dramatically in the final week of 2014 compared to the same week the year before.

Bratton said the department would investigate whether any officers were actually involved in a deliberate work slowdown, but he cautioned against any argument of a widespread conspiracy – noting that half of the city’s officers live within the five boroughs and have families who depend upon the NYPD for their safety.

“If you think that those officers are going to risk the safety of their families, and allow the other officers who don’t live here to risk the safety of their families, I don’t think that’s going to happen,” Bratton said.

Bratton added that he did not agree with the claims from Patrolmen’s Benevolent Union President Pat Lynch that de Blasio had “blood on his hands” in the officer murders due to some remarks critical of police officers’ actions.

“I don’t share that perspective at all,” the commissioner said.

The remarks came after the police unions demanded a public apology from de Blasio.

“The mayor needs to be humble. He needs to realize that his philosophical view of coming into the role of mayor of New York — although it’s his personal view — is not the view of all 8 million people. And he needs to tone that in a different way; channel that in a different way, with some type of an apology,” Sergeants’ Benevolent Association President Edward Mullins told CBS2 Political Reporter Marcia Kramer.

But City Hall sources said the mayor believes he has, in fact, supported the Police Department – first by not bowing to critics and ending the broken windows policy, and second by increasing the NYPD budget.

The mayor invested an additional $352 million for such things as training, handheld mobile devices, security cameras, and rebuilding dilapidated precincts.

The tensions between the mayor and the police unions has drawn the attention of other leaders in the area. New Jersey Gov. Chris Christie spoke out about the issue while appearing on WFAN’s Boomer & Carton radio show earlier Monday.

“I absolutely believe you need to have respect for the office people hold. That’s part of keeping our civil society together. But you can also understand some very emotional reaction from folks who believe that they weren’t served correctly,” Christie said. “So, you know, this is a very, very tough one, and one that, I think, in the end, cooler heads have to prevail on both sides, for people to understand and respect the roles that each play so that we have a peaceful and civilized society which is what people want and expect from everybody who serves in government.”

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