A photo of gunman Ismaaiyl Brinsley was released by police
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.
Brinsley shot them as they sat in their patrol car in Brooklyn before running into a nearby subway station and reportedly shooting himself.
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.
The Rev Al Sharpton, a prominent civil rights activist, said Mr Garner's family had no connection to the gunman and called the killings "reprehensible".
Community leaders have called for peace and the mayor of New York, Bill de Blasio, has ordered flags across the city to be flown at half-mast.
'Self-despair and anger'
Brinsley, 28, had been arrested at least 19 times and had a troubled childhood so violent that his mother was afraid of him, police said.
Liu Wenjin (left) and Raphael Ramos were the police officers killed
People said prayers for the two officers at memorial services in New York
There were prayers and songs at vigils for the officers
A moment of silence was held before a basketball game in Brooklyn
In online postings, he expressed "self-despair and anger at himself and where his life was'', Chief of Detectives Robert Boyce said.
Before the shootings, Brinsley shot and wounded a former girlfriend.
Lucy Ramos, aunt of Rafael: "I hope and pray that we can reflect on this tragic loss...so that we can move forward and find an amicable path to a peaceful co-existence"
The killings come at a tense time, with nationwide protests over the deaths of unarmed black men at the hands of police officers.
At one of the memorials, Lucy Ramos, an aunt of Officer Ramos, said she hoped "we can move forward and find an amicable path to a peaceful coexistence".
The attacks have also put pressure on the New York mayor.
Officers turned their back on him at a news conference, angry at what they saw as his support for protests against the police.