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The family members and supporters of Eric Garner had a message for New York City and the Justice Department on Tuesday: It’s not over.

In two emotional news conferences, Mr. Garner’s family, elected officials and civil rights leaders denounced the decision by federal prosecutors not to bring criminal civil rights charges against the New York City police officer who used a chokehold on Mr. Garner in the moments before he stopped breathing.

“The D.O.J. has failed us,” Mr. Garner’s mother, Gwen Carr, said on Tuesday morning. “Five years ago, my son said ‘I can’t breathe’ 11 times. Today we can’t breathe. Because they have let us down.”