He was taken to a hospital, where he was pronounced dead, an NYPD official told HuffPost.
Gotti died of cancer in prison in 2002.
The Gambino crime operation is one of the five historic Italian-American Mafia families in New York, Reuters has previously reported, and it makes money through violence and extortion.
The Gambino family is one of five mafia families that have always been seen as running Italian-American organized crime syndicates in NY.
Cali, who was born and raised in NY, was the nephew-in-law of John Gambino and the great-nephew of Bonanno mobsters Vito Bonventre and Giovanni Bonventre.
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Cali, the judge wrote, had subjected the victim "to an implied threat of violence" which carried great weight due to Cali's "status in the organized crime family which carries a reputation for violence". There were no arrests and the investigation is ongoing, the NYPD said.
Federal prosecutors in Brooklyn had referred to Cali in court filings in recent years as the underboss of the Gambino organization, related through marriage to the Inzerillo clan in the Sicilian Mafia.
The Gambino operation is said to be one of the five historic Italian-US mafia families in NY.
Paul Castellano also owned a home there.
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Incluso la funcionaria Nahle dijo que su colega de gabinete Arturo Herrera tendrá que rectificar sus declaraciones una vez que arribara a México.
Cali, 53, said to be head of the infamous Gambino crime family, may not have seen the blue pickup truck approaching before it mowed him down.
Following Castellano's murder, Gotti headed the Gambino family until his incarceration for conspiracy and murder in 1992.
Last October, Bonanno crime family associate Sylvester Zottola, 71, was gunned down at a Bronx McDonald's drive-thru as he waited for a coffee. He was shot on a tree-lined street in one of New York City's less-glamorous outer boroughs, a short walk from ball fields, a country club and a day camp.
Last week, Carmine Persico, the 85-year-old former boss of the Colombo organisation, died after serving 33 years of a 139-year prison sentence. One man kneeled down next to Cali's body and sobbed, "Papa!"
Otherwise known as "Franky Boy", Cali was considered the de facto godfather of the Gambino crime family, having served on its ruling panel for several years.
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También, fuentes extraoficiales aseguraron a Excélsior que existen fuertes indicios de que los pasajeros plagiados son migrantes . El autobús, que cubría la ruta Tampico-Reynosa, viajaba con 41 pasajeros , de los cuales sólo 22 llegaron a la terminal.