New York City reached a settlement with the family of Eric Garner on Monday, agreeing to pay $5.9 million to resolve a wrongful-death claim over his killing by the police on Staten Island last July, the city comptroller and a lawyer for the family said.

The agreement, reached a few days before the anniversary of Mr. Garner’s death, headed off one legal battle even as a federal inquiry into the killing and several others at the state and local level remain open and could provide a further accounting of how he died.

Still, the settlement was a pivotal moment in a case that has engulfed the city since the afternoon of July 17, 2014, when two officers approached Mr. Garner as he stood unarmed on a sidewalk, and accused him of selling untaxed cigarettes. One of the officers used a chokehold — prohibited by the Police Department — to subdue him, and that was cited by the medical examiner as a cause of Mr. Garner’s death.

The killing of Mr. Garner, 43, followed by the fatal shooting of Michael Brown by a police officer in Ferguson, Mo., in August, set off a national debate about policing actions in minority communities and racial discrimination in the criminal justice system.

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