A grand jury has not charged a New York City police officer over the death of Eric Garner, who died after being placed in a chokehold by the officer.
A video of Officer Daniel Pantaleo arresting Garner on 17 July sparked national attention.
Asthmatic Garner, 43, was heard on the video shouting "I can't breathe!"
Following the grand jury decision, President Barack Obama said it "speaks to larger issues" US minorities have with law enforcement.
The president was one of a number of people to appeal for calm, as the decision came just a week after another grand jury in Missouri did not charge a police officer who killed a black teenager in Ferguson.
That decision sparked riots in Ferguson and protests across the country.
This week, US President Barack Obama sought emergency funding to improve police training and to restore trust in policing.
Esaw Garner, wife of Eric Garner, breaks down into the arms of Rev Al Sharpton
New York Mayor Bill de Blasio called the grand jury outcome "one that many in our city did not want" and appealed for a "peaceful, constructive" response.
Protests have been organised in the New York neighbourhood of Staten Island, where Garner was arrested, for Wednesday evening.
Garner family lawyer Jonathon Moore said he was "astonished" by the decision.
Eric Garner's daughter, Erica Sniper, told the BBC the grand jury "are not even human, [and] there is no humanity".
"On that video you can see the most cruel horrible thing that someone could do to someone," she added. "It's just not right."
Mr Pantaleo issued a statement in which he said he was praying for Garner and his family.
"It is never my intention to harm anyone and I feel very bad about the death of Mr Garner," he said.
"I became a police officer to help people and to protect those who can't protect themselves."
US Senator Kirsten Gillibrand called Garner's death a "tragedy that demands accountability".
"Nobody unarmed should die on a New York City street corner for suspected low-level offenses," she said.
"I'm shocked by this grand jury decision, and will be calling on the Department of Justice to investigate."
A woman places flowers at a memorial near the site of Eric Garner's death
Mobile phone video of the incident shot by a witness showed Garner verbally refusing to be handcuffed.
Mr Pantaleo responded by putting Garner in an apparent chokehold, which is banned under New York Police Department policy.
A second video, apparently filmed shortly after the incident, shows Garner lying on the sidewalk.
Three minutes into the video, medics arrived and he was lifted into an ambulance.
A bystander asked why no-one was trying to resuscitate him and one officer responds, "because he's breathing". Garner died shortly afterwards.
The city's medical examiner's office has said Garner's death was caused by "the compression of his chest and prone positioning during physical restraint by police", but said other factors contributing to his death included asthma and heart disease.