Cali was rushed to Staten Island University Hospital North and declared dead, the sources said.
The Gambino operation is said to be one of the five historic Italian-US mafia families in NY.
At this time, police have made no arrests and Cali's death is under investigation. But Cali told his brothers that while he was moved by their support, he would not accept the promotion to run the family's billion-dollar concerns.
'The man was on the ground face-up. "His head was by his SUV, and the truck was open", the witness told the outlet.
One woman yelled into her phone, "Why doesn't the ambulance come?"
John Gotti, who organised the hit, then took power at the helm of the Gambino family.
AFP 2018 OLIVIER MORIN'Mafia Can't Become Extinct Because It's a Type of Behaviour- Criminologist
After his release, the feds tried to bar him from meeting with members of the Sicilian Mafia, and demanded that he avoid contact with his uncle, Giovanni Gambino - the nephew of late boss Carlo Gambino, for whom the family was named - except at weddings or holiday celebrations approved in advance.
The organization reportedly focused its efforts on heroin and Oxycontin trafficking under his leadership.
The Gambinos" rise to become one of the most powerful mafia families in America started in 1957, when the family's namesake, Carlos Gambino - an Italian immigrant - orchestrated the murder of Albert Anastasia, who had organized a collection of Italian gangs into what now would be considered a "crime family'. Paul Castellano also owned a home there.
Charges against members of Mafia operations, including Gambino family operatives, have included murder, loan sharking, gambling and illegal drug distribution, Reuters has reported.
The Gambino family was once considered the biggest organised crime group in the United States, the New York Times reports, but began to decline after Gotti and other senior figures were jailed. John Gotti and his turncoat underboss, Sammy "Bull" Gravano watched the action from Third Avenue.
8 killed in mass shooting in southern Brazil school
Despite strict weapon laws, gun crime is rampant in Brazil, yet school shootings are a rare occurrence. About 1,000 children attend the school, police said. "The school is on lockdown", he said.