Pirro, whose body will lie in state at the Casa del Cinema film institute on Saturday, died in his apartment.
Pirro enjoyed Oscar success in the early 1970s when his films won the best foreign language award and he was nominated twice for his writing.
Rome's mayor, Walter Veltroni, paid tribute to Pirro's "extraordinary talent" for interpreting society.
Mr Veltroni, a former film critic, paid tribute to "one of the greatest screenwriters in the history of cinema".
Indagine Su Un Cittadino al Di Sopra Di Ogni Sospetto - or Investigation of a Citizen Above Suspicion - won best foreign language film in 1971.
And Giardino dei Finzi-Contini - or Garden of the Finzi-Continis - won the same Oscar in 1972.
During his career, Pirro adapted a number of Mafia novels written by Sicilian author Leonardo Sciascia.
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