"There are no arrests and the investigation is ongoing", a statement said.
There was also a report of a blue pickup truck leaving the scene around that time.
Cali was taken to a hospital where he was pronounced dead.
They said distraught family members ran outside after the shots were fired. His head was by his SUV, and the truck was open'.
USA media reported that his death marked the first murder of a NY mob boss in 34 years, since the death of Paul Castellano - another Gambino family boss - by order of John Gotti.
According to local media in NY, he took the helm of the Gambino family in 2015, replacing Domenico Cefalu.
Cali had been considered a unifying figure in the years after John Gotti, "Dapper Don", was convicted and sent to prison by cooperating mob witnesses, CNN affiliate WPIX reported.
His only criminal conviction came in 2008, when he pleaded guilty to an extortion conspiracy charge resulting from a failed bid to build a NASCAR track on Staten Island years earlier.
Cops retrieve evidence from the scene where Mob boss Francesco Cali was clipped late Wednesday. THE ASSOCIATED PRESS
"Within recent months one of John Gotti brothers, Eugene Gotti, came out of federal prison".
It had been decades since a Mafia boss was hit in NY.
Gambino crime boss Francesco "Franky Boy" Cali was assassinated in front of his Staten Island home Wednesday night in a stunning gangland hit that recalled some of the most infamous Mafia killings in city history. "The word that I'm hearing is this: That there's old school tension and friction".
New York's major crime families, the Gambinos, the Luccheses, the Genoveses, the Bonannos and the Colombos, have seen some decline over the past few decades, as federal law enforcement agencies have tried to extricate their influence from construction and other major industries.
Gambino headed the organization until 1976, when he handed power over to his brother-in-law Paul Castellano.
Cali then reaches into his trousers pocket to insinuate that he had a gun, the law enforcement source told the Daily Beast.
In that case, authorities intercepted conversations shedding light on his quiet underworld command.