Protesters have rallied in US cities for a third night to denounce police treatment of black Americans.

The wave of largely peaceful demonstrations across the country including New York, New Jersey, Colorado and Florida, follow the decision by a grand jury not to indict a white policeman in the chokehold death of a black man, Eric Garner.

In one protest a group of more than 100 people stormed into a Manhattan Apple Store chanting slogans before staging a "die-in" as shoppers and employees looked on.

There was no looting or vandalism, and the group left, with no arrests, after about five minutes.

Nationally, tensions were already running high after a white policeman was cleared in the fatal shooting of the unarmed black 18-year-old Michael Brown in Ferguson, Missouri.

The latest fatal shooting of a black man, Akai Gurley (28) by a cop on a housing project stairwell in Brooklyn has only served to fuel public outrage, and stoke the debate about race, policing and the justice system.

A New York City prosecutor has said he would convene a grand jury to consider charges against the officer.

There have also been protests in Phoenix, Arizona, after a white police officer shot dead an unarmed black drug suspect during a scuffle.

And in Ohio, the family of a 12-year-old boy who was carrying a pellet gun when he was shot dead by a police officer has filed a wrongful-death lawsuit.

Mr Garner, a father of six, died after he was restrained with an apparent chokehold while being arrested on suspicion of selling untaxed cigarettes on Staten Island in July.

A viral video shot by an onlooker showed the 43-year-old, who had asthma and a heart condition, repeatedly gasping "I can't breathe!". He later died in hospital.

President Barack Obama has also weighed into the debate, saying "too many Americans feel deep unfairness when it comes to the gap between our professed ideals and how laws are applied on a day to day basis".