Eric Garner's death in July 2014 was the first in a year of high-profile, racially-charged incidents in which white officers have been accused of using unreasonable force or being too quick to fire at black suspects.
The deaths have fueled nationwide protests, bitter debate about racism and demands for structural reforms to police practices.
The city of New York announced a settlement with the Garners on Monday, nine months after the family took steps towards seeking $75 million in damages.
Garner's loved ones and civil rights campaigner Al Sharpton urged the US federal government at a news conference to take up the case and to hold the white police officers accountable for his death.
"This does not represent justice. We call on the Department of Justice and (US Attorney General) Loretta Lynch to deliver justice for my father," said daughter Erica Garner.
"Justice is indictments and a fair trial."