Sharpton said the ruling is "probable cause" for the quick arrest of Officer Daniel Pantaleo, the white police officer who used the chokehold on Garner, who is black, on July 17 on Staten Island.
Sharpton said the Staten Island district attorney, Daniel Donovan, "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."
Donovan's office did not immediately return a message left Saturday. On Friday, a spokesman said 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.
Pantaleo's attorney, Stuart London, did not immediately return a message left Saturday. He declined to comment Friday.
Sharpton announced an Aug. 23 march across the Verrazano Bridge between Brooklyn and Staten Island to demand justice for Garner. He said the date was chosen because it is the 25th anniversary of the shooting death of Yusuf Hawkins, a black 16-year-old, at the hands of whites in Brooklyn.
"We cannot go back 25 years," Sharpton said. "Twenty-five years later in the name of Eric Garner we are going forward."
Garner's arrest and his final pleas of "I can't breathe!" were videotaped.
The medical examiner 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.
Police Commissioner Bill Bratton has said the New York Police Department'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 police union, Patrick Lynch, said that if Garner "had not resisted the lawful order of the police officers placing him under arrest, this tragedy would not have occurred."
Associated Press writers Eric Tucker in Washington and Jake Pearson, Jonathan Lemire and Vanessa A. Alvarez in New York contributed to this report.
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