NEW YORK (AFP) - Thousands of demonstrators marched in major cities across the United States on Friday in a fresh wave of protest against the killing of unarmed black men by white police officers.

The latest rallies in a fortnight of growing discontent took place as a New York prosecutor said he would impanel a grand jury to consider charges in one of the cases that has again brought to the fore the distrust felt by many African Americans towards the police.

Akai Gurley, 28, a father of a young daughter, was shot dead when a police officer opened fire in a dimly lit staircase at a Brooklyn apartment building as he walked with his girlfriend late on Nov 20.

Brooklyn District Attorney Ken Thompson said he would present all the evidence for a grand jury to decide whether charges should be brought.

"It is important to get to the bottom of what happened," he said, giving no timetable for the jury to be appointed, nor for a decision to be reached.

"I pledge to conduct a full and fair investigation and to give the grand jury all of the information necessary to do its job. That information is still being gathered," Thompson said.

New York's police commissioner has said Gurley was a totally innocent victim and the family, who gathered for a private wake on Friday night ahead of the funeral on Saturday, has demanded justice.

Protesters hit the streets in recent days after grand juries declined to press charges against white officers responsible for the August 9 shooting death of unarmed 18-year-old Michael Brown in Ferguson, Missouri, and the July 17 chokehold death of black father-of-six Eric Garner in New York.

Several hundred protesters again staged rallies in New York on a rainy Friday night, one in Columbus Circle that moved to Fifth Avenue, and the second walking up Broadway from the south.

Similar protests were reported elsewhere across the United States including in Miami, Chicago, Boston, New Orleans and Washington, DC.

It was the first time the demonstrations demanding justice had taken to the streets in Miami, where protesters blocked traffic, while in the US capital some people staged a "die-in" on the roads.

- 'He loves his baby girl' -

The decision last week in the Ferguson case sparked looting and arson in the St Louis suburb, while outrage over the Garner case has been the rallying cry for the latest protests.

On Thursday, demonstrators blocked roads, tunnels and bridges, and shouted "I can't breathe." Those were the final words gasped by Garner, a 43-year-old asthma sufferer, as police wrestled and held him to the ground in New York's State Island.

In the Gurley death, family representative Kevin Powell said the recent cases feel "like a series of modern-day lynchings."

Gurley's mother Sylvia Palmer paid tribute to her son. "He hasn't done nothing wrong. He's a good man, good, he loves his family, he loves his baby girl," she said.

"He was going to bring home my granddaughter to visit me for the first time."

Pallbearers carried Gurley's coffin in the rain from a hearse into the Brown Memorial Baptist Church in Brooklyn for a wake, followed by a funeral service on Saturday at 11:00 am.

"My son was my sunshine and my wife's sunshine," said Gurley's stepfather Kenneth Palmer.

"He was not only a son, he was a brother, he was a nephew, he was a friend, he was a father."

- 'Negligence' -

The New York Daily News reported that the officer who fired the fatal bullet texted his union representative as Gurley lay dying.

After rookie cop Peter Liang discharged the bullet that struck Gurley, he and partner Shaun Landau did not respond to radio contact for more than six-and-a-half minutes, the newspaper said.

"That's showing negligence," it quoted a law enforcement source as saying of the pair's decision to text their union rep before making a radio call for help.

A neighbour instead phoned for the ambulance that rushed Gurley to hospital, where he was declared dead on arrival.

New York Police Commissioner Bill Bratton said on Nov 21 that Gurley was an innocent who had been killed by an "accidental discharge" in an "unfortunate tragedy."

Civil rights activist Al Sharpton's National Action Network is scheduled to hold another rally outside its national headquarters, The House of Justice, in Harlem, New York, on Saturday morning.

Despite the protests, New York Mayor Bill de Blasio said that general complaints of police misconduct fell 26 per cent from July to November and allegations of excessive force declined 29 per cent.