Those elements — combined with Mr. Mullins’s remarks — could pose a challenge for Mr. de Blasio, a Democrat in his second term who has struggled to get along with the city’s police force. Officers famously turned their backs on the mayor in 2014 at the funeral of Rafael Ramos, one of two officers killed in an ambush.

Mr. Cuomo, a Democrat who pushed for more officers on the subway, said on Monday that the tension between the police and the community was “dangerously frayed,” worse than he could remember.

“You’d have to go back decades to find this kind of stress between the police and the community,” the governor said in a radio interview. “It’s something that has to be addressed.”

During his mayoralty, Mr. de Blasio has sought to repair his relationship with the police, and the tension had appeared to wane in recent years.

But Eugene J. O’Donnell, a former officer who teaches at John Jay College of Criminal Justice, said the relationship never fully healed. He cited the city’s firing last year of Daniel Pantaleo, the officer whose chokehold led to the death of Eric Garner on Staten Island in 2014.