Eric Garner's mother, Gwen Carr, said she was grateful for the medical examiner's report saying Garner's death was caused by a banned police maneuver.
Carr and other family members spoke to supporters at the Harlem headquarters of the Rev. Al Sharpton, who said prosecutors should make an arrest in Garner's death.
Sharpton said the district attorney of Staten Island, where Garner died July 17, "needs to say, 'I'm moving forward to an arrest' or 'I'm deferring to the federal government.'"
Garner's widow, Esaw Garner, added, "I just want them to do the right thing and give me justice for my husband."
Sharpton announced a planned Aug. 23 march across the Verrazano Bridge between the boroughs of Brooklyn and Staten Island to demand justice for Garner.
The gathering at Sharpton's headquarters came the day after the medical examiner's office ruled that Garner was killed by neck compressions from the chokehold and "the compression of his chest and prone positioning during physical restraint by police."
Asthma, heart disease and obesity were contributing factors in the death of the 43-year-old Garner, a 6-foot-3, 350-pound father of six, the medical examiner said.
His videotaped arrest and final pleas of "I can't breathe!" sparked outrage and led to the overhaul of use-of-force training for the nation's largest police department.
Carr said Saturday that since her son's death, she's been waking up at night screaming, "Let him go! Give him air."
The confrontation between the white police officer who used the chokehold, Daniel Pantaleo, and Garner, who is black, had prompted calls by Sharpton for a federal civil rights investigation.
Pantaleo's attorney, Stuart London, declined to comment Friday.
Chokeholds are prohibited by the New York Police Department, but partial video of the confrontation shows an officer placing a chokehold on Garner, who was being arrested on suspicion of selling untaxed, loose cigarettes. Garner then apparently loses consciousness.
A spokesman for Staten Island District Attorney Daniel Donovan said Friday that prosecutors were still investigating the death and awaiting a full autopsy report and death certificate from the medical examiner. Donovan will have to determine whether to empanel a grand jury and file charges.
Federal officials are monitoring the investigation but have not begun their own inquiry, a Department of Justice spokeswoman said.
Police Commissioner Bill Bratton has said the NYPD's use-of-force training is lacking and has pledged to retrain all 35,000 officers.
Pantaleo was stripped of his gun and badge pending the investigation, and another officer was placed on desk duty. Two paramedics and two emergency medical technicians were suspended without pay.
The president of the powerful Patrolmen's Benevolent Association, Patrick Lynch, expressed his sympathies to Garner's family but noted Garner "was a man with serious health problems."
"We believe, however, that if he had not resisted the lawful order of the police officers placing him under arrest, this tragedy would not have occurred," he said.