The man who shot dead two New York police officers told members of the public "watch what I'm going to do" shortly before the attack, police say.
Ismaaiyl Brinsley, 28, had a history of violence and mental instability.
Candlelit vigils have been held in New York in memory of the two officers, Liu Wenjin and Raphael Ramos, the BBC reports.
Brinsley shot them as they sat in their patrol car in Brooklyn before running into a nearby subway station and reportedly shooting himself.
Chief of Detectives Robert Boyce said Brinsley, 28, had "no history of radicalisation" but that he was "often violent" and had been arrested at least 19 times.
He had posted messages on social media saying he would kill police officers in retaliation for the death of Eric Garner, a black man who died when white police officers arrested him.