Brinsley, who had a long arrest record and history of mental problems, fled on foot, threatening two power utility workers who chased him in their vehicle, before shooting himself dead in a nearby subway station as armed officers arrived.
The murders followed weeks of nationwide protests over police tactics following decisions by grand juries in New York and Missouri not to prosecute white officers in the killings of Eric Garner and Michael Brown.
In New York, police chiefs ordered foot patrols to work only in pairs, posted sentries outside stations, suspended operations by unarmed auxiliary officers and redeployed detectives in teams of three or more. Officers were warned to wear bullet-proof vests and to cut back on unnecessary contact with the public, and to take extra caution in responding to calls for help. Similar directives were implemented across the US.
The policies have fuelled a sense of siege and are a setback for New York police chiefs, who have been working to put more officers on patrol as they develop community policing practices.
In a message urging the 35,000 officers in his force, the nation's largest, to "be safe", Bill Bratton, the New York police chief, said of the dead men: "They were assassinated - targeted for their uniform."
Public plea
Mayor Bill de Blasio pleaded for a pause in protests and rancour amid a widening rift with those in a grieving police force who accuse him of creating a climate of mistrust that contributed to the killings of two officers.
De Blasio called for a halt of political statements until after the funerals of the slain officers, an appeal to both sides in a roiling dispute centred on the deaths of unarmed black men at the hands of white police officers.
"We are in a very difficult moment. Our focus has to be on these families," de Blasio said at police headquarters, referring to the families of the two slain police officers.
De Blasio's relations with the city's police unions have tumbled to an extraordinary new low.
The mayor tried to strike a unifying note in his first extensive question-and-answer session since the shooting.
He said he was confident the city was "working toward a day where we can achieve greater harmony toward policing and community".
- AP