A grand jury in December declined to indict the officer, Daniel Pantaleo, who placed Garner, 43, in the chokehold, a maneuver banned by the New York City Police Department. A video that a bystander took of the incident sparked protests across the country over police treatment of minority groups.
After the state grand jury declined to indict, then-U.S. Attorney General Eric Holder in December promised a full investigation into Garner's death.
Nearly one year after Garner's death on New York's Staten Island borough, his widow, Esaw Garner, his mother, Gwen Carr, and three of his children held a press conference on Tuesday in New York alongside civil rights leader Reverend Al Sharpton.
They called for charges in connection with his death.
"We are losing our family members and they are not losing anything," said Garner's wife, Esaw, who more than once broke down in tears. "Now I am alone to deal with this my whole life."
Garner, a father of six, was accused of illegally selling cigarettes on a sidewalk when Pantaleo put him in the chokehold from behind and brought him down with the help of other officers. Garner complained repeatedly that he could not breathe.
The city medical examiner ruled Garner's death a homicide, with asthma and obesity as contributing factors.
New York City agreed to pay Garner's family $5.9 million to resolve the claim over his death, officials said on Monday.
The Garner settlement is among a series of large settlements agreed to over the past two years by City Comptroller Scott Stringer and Mayor Bill de Blasio to resolve cases of alleged police brutality.
A separate settlement was reached with the hospital that employed emergency medical technicians who responded to the scene and did not aid Garner. Terms of that agreement have not been released.
Garner's family had filed a claim in October seeking $75 million in damages.
"The settlement that we got isn't a victory," said Garner's mother, Carr. "The victory will come when we get justice. Where is the justice?"
Tuesday's press conference was the first of a number of events marking the Friday anniversary of Garner's death.
De Blasio will speak at a Tuesday evening service at the Mount Sinai United Christian Church on Staten Island. The list of attendees includes New York Cardinal Timothy Dolan, who beforehand is slated to visit the nearby NYPD 120th Precinct, home to the officers involved in the incident.