The New York Daily News reports that a panicked family member called 911 and told the dispatcher that Cali was run over before he was shot, although investigators were still looking into whether the gunman mowed the mobster down.
Cali was "a real quiet old-school boss", a police source told The New York Post.
No arrests have been made.
"The Gambino crime family during Castellano's reign was the largest criminal organization in the US, with law enforcement estimating it had some 250 "'made" members" and "more than 550 lower-ranking "associate' members".
The body of former mob boss John Gotti is carried from Papavero Funeral Home in the Queens borough of NY 15 June 2002.
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The Gambino criminal organisation is one of the "Five Families" of organised crime in NY, alongside the Bonanno, Colombo, Genovese and Lucchese families.
"There are no arrests and the investigation is ongoing", a statement said.
According to reports, Cali's death marks the highest ranking member of a NY crime family to be murdered in decades.
DeCicco was the No. 2 figure in the Gambino family in 1986 when he died in a auto bombing in Brooklyn.
"Frank Cali was a pretty likeable guy, and also this is not a way the mob would kill one of their own", he said.
He had long ties with the Sicilian mafia and the Gambino family, and was said to have intentionally kept a low profile during his time in charge.
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Paul Castellano, the Gambino family head at that time, was shot in the street on Manhattan's East Side.
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". Today's news is a big flashback to those days.
Cali, who served on the family's ruling panel for several years, was elevated to acting boss in 2015, replacing then 68-year-old Domenico Cefalu.
Last October, Sylvester Zottola, 71, reportedly of the Bonanno crime family, was gunned down at a McDonald's drive-thru in the Bronx.
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.
"Papa! Papa!" one man cried before laying down on the grass, sobbing, the witness recounted.
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