Akai Gurley, a 28-year-old black man, was shot in the chest after he entered the stairwell of his apartment building.
A grand jury will be asked whether to prosecute the officer responsible.
The move comes days after a grand jury decided not to charge another New York policeman over the chokehold death of another unarmed black man, Eric Garner, sparking protests across the country.
The US was already facing race-related unrest over the decision not to indict a white police officer who had shot dead a young black man, Michael Brown, in Ferguson, Missouri.
The funeral took place at Brown Baptist Church in Brooklyn on December 6.
Akai Gurley’s mother, stepfather and two-year-old daughter were among those who attended the service.
Activist Kevin Powell delivered the eulogy for Akai Gurley.
“Akai was innocent, innocent, innocent,” he said.
“This is modern-day lynchings, over and over again. Akai Gurley was simply the latest victim of this,” he added.
The funeral featured music from gospel singers and a poem read by Akai Gurley’s younger brother.
Protests against police violence towards minorities continued on December 6 for a fourth day.
The latest spate of protests was sparked by the decision by a grand jury not to charge a New York policeman over the death of Eric Garner, who died after police put him in a chokehold.
Hundreds streamed along Fifth Avenue and other parts of Manhattan on Friday evening , with banners and chants of “Black lives matter” and “I can’t breathe” – a reference to Eric Garner’s last words.
In announcing the grand jury – a body that determines whether to bring criminal charges – Brooklyn’s District Attorney Ken Thompson said it was important to conduct a full and fair investigation.
Police say Akai Gurley and his girlfriend had opened a door into the unlit stairway and an inexperienced officer on a routine patrol fired his gun.
New York Police Commissioner William Bratton called the shooting an accident. However, the medical examiner has ruled that the death is a homicide.
Civil rights leader the Reverend Al Sharpton had initially planned to speak at Akai Gurley’s memorial service but later said he would pay his respects without making an address.
Activists have called for another march in Washington on December 13, followed by a summit on civil rights.
Mg0Fz7omc1EImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…