New York City’s mayor praised its police department for helping bring crime rates down in 2014, calling it the “world’s greatest police department” during a press conference on Monday, in the wake of controversy that saw hundreds of officers turn their backs to him as he spoke during the funerals of two slain detectives in Brooklyn.

Responding to police protests at the latest of those funerals, on Sunday, mayor Bill de Blasio called the actions by some NYPD officers “disrespectful” and police commissioner Bill Bratton said those involved “embarrassed themselves”, during a joint news conference held at police headquarters to review the year-over-year crime statistics.

“Those individuals who took certain actions the last two weeks, they were disrespectful to the families involved. That’s the bottom line,” de Blasio said. “They were disrespectful to the families who lost their loved ones. I can’t understand why anyone would do such a thing in the context like that.”

Wenjian Liu, 32, and his partner, Rafael Ramos, 40, were shot dead as they sat in their patrol car on a street corner in Brooklyn last month. The gunman, troubled 28-year-old Ismaaiyl Brinsley, shot himself dead shortly afterward. Officers turned their backs on the mayor as he gave the eulogy during Ramos’s funeral last week, and – despite being implored by Bratton to not do it again – they did it at Liu’s funeral on Sunday.

“What was the need, in the middle of that ceremony, to engage in a political action?” Bratton said. “I don’t get it and I’m very disappointed … in those who did not respond to my request.”

The deaths of Liu and Ramos, who were posthumously made detectives, has exacerbated already strained relations between the mayor, the police department and protesters demanding reforms in the wake of the death of Eric Garner last year.

Some NYPD officers have accused the mayor of inflaming anti-police sentiments by seemingly condoning criticism of the department after a grand jury failed to indict the white NYPD officer implicated in the death of Garner, a black Staten Island man. Following the non-indictment, de Blasio said during an emotional speech that he had to “train” his biracial son on how to behave during encounters with the police.

Bratton has steadfastly defended the beleaguered mayor against such criticism.

“I don’t share the perspective that the mayor had blood on his hands,” Bratton said.

Meanwhile, some NYPD officers have reportedly engaged in a work “slowdown”. According to the New York Times, NYPD officers arrested fewer than half as many people and wrote more than 90% fewer summonses than in the same two-week period one year ago.

Bratton said a task force has been assembled to determine if there is a calculated work stoppage underway or if the declines are attributable instead to a combination of the holidays and a change in policing schedules due to the events of recent weeks. He said if there is a deliberate slowdown, those shirking their policing duties would be dealt with “very forcefully”.

“I haven’t used the word ‘slowdown’,” Bratton said. “If that’s what it is, we’ll call it that and deal with it accordingly. We’re not in a public-safety crisis in any shape of the word,” he said.

During the press conference, the mayor announced that crime in New York fell by 4.6% in 2014, with homicides at a modern-day low of 332. But against the drama of the past few weeks, the news seemed a well-timed opportunity for de Blasio to praise the police force with which he is increasingly at odds.

Concluding, DeBlasio said: “As we begin the new year, we will build on last year’s momentum to ensure the world’s greatest police department keeps getting better, and to ensure we keep our residents and our officers safe from harm.”