The largely peaceful demonstrations came as details emerged of another racially-tinged death.
America's largest city of 8.4 million again saw bursts of outrage after a grand jury on Wednesday decided not to indict a white officer for the death by chokehold of an unarmed black father-of-six.
Demonstrators blocked roads, tunnels and bridges, with many of them shouting "I can't breathe" - the words that heavy-set asthma sufferer Eric Garner, 43, gasped repeatedly as police wrestled and held him to the ground during his arrest in July for selling un-taxed cigarettes. 
Video of the arrest has been aired repeatedly on TV. Garner, a father of six, died of what was called a heart attack.
Dozens of people were arrested in Thursday's rallies, the New York Times reported, quoting police.
Demonstrations were also held in Chicago, Boston, Philadelphia, Baltimore and Washington DC, where they snarled traffic near the White House as President Barack Obama lit the national Christmas tree.
As helicopters hovered above, thousands of activists massed in New York's Foley Square, near the city police headquarters shouting "Shut it down" and carrying placards saying "Black Lives Matter" and "Racism Kills."
"We cannot tolerate police impunity. The government has to do something. They have a video showing what happened," said a 40-year-old demonstrator who gave his name only as Jonathan.
Police sealed off the Holland Tunnel, the key road link into New Jersey as US media reported that thousands streamed up the west side of Manhattan, clogging streets in downtown Manhattan and shutting traffic on the Manhattan Bridge heading to Brooklyn.
Another group marched across the Brooklyn Bridge, with a black banner that said "this stops today" and 10 black coffins inscribed with names of people killed by police in different city boroughs.
Hundreds then continued the march through Brooklyn, followed by police but a reporter saw no incidents of unrest.
National controversy over Garner's death and a series of other incidents were fanned further on Thursday by a damning US federal investigation which concluded that police in Cleveland routinely employ "excessive force."
In Arizona meanwhile, police said a white officer shot dead a 34-year-old black man during a confrontation outside a convenience store.
Phoenix police said the officer involved shot dead Rumain Brisbon after mistakenly believing he was reaching for a gun inside his jacket. In fact he was unarmed.
The killing is the latest of several cases since the death of Garner which have triggered a national debate about how minorities are treated by police and the American criminal justice system.
Police shot dead a 12-year-old boy in Cleveland last month while another grand jury last week decided not to prosecute a white officer in Ferguson, Missouri who killed unarmed black teen Michael Brown in August.
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