“I can’t breathe,” protesters chanted, in mostly peaceful demonstrations that brought longstanding strains over race to the heart of America’s most populous city. Eighty-three arrests were made during the protests overnight, an NYPD spokesman confirmed to the Guardian. 

Earlier in the day, prosecutors announced the jury’s decision not to charge Daniel Pantaleo, one of the New York police department officers who had confronted Garner for selling loose cigarettes on Staten Island in July.

The protesters’ anger echoed the tensions in Ferguson, Missouri, the scene of violence and rioting after another grand jury declined to bring charges against a white police office in the killing of Michael Brown, an unarmed black teenager suspected of robbing a convenience store. His death sparked hundreds of protests across the country and snapped into focus seething race issues.

Garner, who was black, died in July after being put in a chokehold by Pantaleo. Police had stopped the heavy-set father of six on suspicion of selling untaxed “loose” cigarettes. Garner had been arrested previously for selling untaxed cigarettes, marijuana possession and false impersonation.

A video shot by a bystander shows Garner resisting arrest as a plainclothes officer attempts to handcuff him. Backing away from the officer, Garner tells him: “This stops today,” which has become a rallying cry for protesters in New York. After a struggle during which Garner is wrestled to the ground by several officers, he gasps “I can’t breathe” until his 350lb body goes limp.

President Barack Obama, criticized for his response to unrest in Ferguson, suggested the Garner case had reaffirmed his determination to ensure all Americans are treated equally in the criminal justice system.

“When anybody in this country is not being treated equally under the law, that’s a problem,” the president said in Washington. “And it is my job as president to help solve it.”

After the decision not to bring criminal charges in New York, the US attorney general, Eric Holder, announced a federal investigation. “All lives must be valued,” Holder said. “All lives.”

Holder’s announcement was not enough to placate the anger in the city. About 200 protesters partially closed the West Side Highway, before police made several arrests, while other groups descended on various locations in midtown Manhattan, including Grand Central station, the Lincoln tunnel and Brooklyn bridge. Protesters also targeted the annual lighting of the Christmas tree at the Rockefeller Center, but were kept away from the ceremony.

As crowds rallied in Times Square, one young black man likened the treatment of minorities in the US in the 21st century to the early days of slavery. “It goes back to the foundations of the country. We’ve been dehumanised since we’ve been here, and we are being dehumanised now,” he said.

“Every 28 hours a young black man is killed by police,” one young woman told the Guardian, referring to nationwide statistics. “Only 2% of police are indicted. Those numbers are crazy. It’s telling young black men that their lives don’t matter and their deaths can be passed over.”

Groups of protesters continued marching well into the night.

The mayor of New York, Bill de Blasio, had earlier urged calm. De Blasio, who is white, said that he and his wife, Chirlane McCray, who is black, had spent years teaching their mixed-race son, Dante de Blasio, 17, how to “take special care” around police officers.

We “have had to [talk to] Dante for years about the dangers he may face,” de Blasio said in an emotional news conference. “Because of a history that still hangs over us, we’ve had to train him, as families have … in how to take special care in any interaction with the police officers who are there to protect him.”

The mayor called on protesters to remain nonviolent, saying he had just met Ben Garner, Eric Garner’s father. “Eric would not have wanted violence,” the mayor quoted the father as saying.

De Blasio acknowledged the widespread discontent the grand jury decision was likely to cause. “It’s a very emotional day for our city,” he said. “It’s a very painful day for so many people of this city.” The mayor said the country was at a crossroads, calling discrimination and inequality before the law “all our problem”.

“Anyone who believes in the values of this country should feel a call to action right now,” De Blasio said. “It is a moment that change must happen.”

Minutes later, Garner’s family appeared alongside civil rights campaigner the Rev Al Sharpton in Harlem to address the media.

Garner’s widow, Esaw, vowed to continue fighting for justice. “As long as I have breath in my body I will fight the fight,” she said.

In Washington, Holder said that Garner’s death as well as that of unarmed teenager Brown, who was shot dead by police officer Darren Wilson in Ferguson in August, “have tested the sense of trust between law enforcement and the communities they are charged to serve”.

Holder said he respected the rights of protesters to voice their disappointment but called on them to remain peaceful.

Tensions had been simmering all week as New Yorkers braced for the verdict.

Activists called for a day of action following the verdict to protest the decision not to pursue charges against Pantaleo. Protesters have also been demanding an end to a policing philosophy championed by NYPD commissioner William Bratton. The policing model, known as broken windows, emphasises attention to petty crime – such as selling untaxed cigarettes – as a means of stymying large-scale crime.

The decision may compound already frayed relations between the New York police department and minority communities, which Bratton and de Blasio have pledged to repair.

The NYPD banned chokeholds over two decades ago, because they can be deadly if administered inappropriately or carelessly. Still, between January 2009 and June 2014, the city’s Civilian Complaint Review Board, an independent agency that investigates police misconduct, received 1,128 civilian complaints involving chokehold allegations. Of these, only a small fraction of the cases are ever substantiated– just ten over the five and a half year window.

In the days after Garner’s death, Bratton said all 35,000 officers would be retrained on the department’s use of force policy.

Sharpton announced a rally in Washington on 13 December. “It’s time for a national march to deal with a national crisis,” he said. “We are not going away.”

Additional reporting by Mae Ryan and Ana Terra Athayde in New York.