An ornate hearse pulled by six black horses carried the coffin to the church
Italian politicians denounced the ostentatious send-off for Vittorio Casamonica, 65.
Banners outside the San Giovanni Bosco church on the city?s outskirts described him as the ?King of Rome?.
The priest said he had no control over what happened outside the church.
It comes amid a spiralling mafia investigation in the capital, in which local criminal bosses allegedly worked with city officials to secure lucrative public contracts.
Hundreds of tearful mourners gathered to pay their final respects to Casamonica, who reportedly died of cancer.
Officials identified him as one of the leaders of the Casamonica clan, which has been accused of racketeering, extortion and drug trafficking.
Politicians said the Hollywood-style funeral sent ?a clear message of impunity? and demanded action to stop such events being used to honour criminal gangs.
A gilded horse-drawn coach carried Casamonica?s body to the church, where mourners were showered with red rose petals.
?You conquered Rome, now you?ll conquer paradise,? read one banner affixed to the building?s entrance.
The coffin was carried inside to the theme tune from The Godfather trilogy, which follows the rise and fall of a fictional Corleone Mafia family.
?Never again. Rome cannot be defaced by those who want it to became the set of the Godfather,? Matteo Orfini, president of the ruling Democratic Party, said on Twitter.
Rome Mayor Ignazio Marino, who has previously refused to resign over the current anti-mafia probe, said he had called Rome?s prefect demanding to know how such a scene could have taken place
He said it was ?intolerable that funerals are used by the living to send mafia messages?.
Meanwhile Arturo Scotto and Celeste Costantino, of the Left Ecology Liberty (SEL) party, called on Interior Minister Angelino Alfano to explain how such a funeral could take place.
?These funerals might seem like a folkloric custom, but in reality, they send a clear message of impunity on the part of the clans: we still exist and we are powerful,? they said in a statement (in Italian).
Some 100 people are being investigated as part of the ?Mafia Capital? inquiry into allegations that elected officials and business figures were part of a crime syndicate targeting Rome contracts.
Commentators noted that Thursday?s funeral took place at the same church where in 2006 the Archdiocese of Rome blocked a ceremony for Piergiorgio Welby, then a symbol of Italy?s right-to-die movement.