Casamonica's daughter and grandson were interviewed on the current affairs show, Porta a Porta, on Tuesday night, during which they defended the funeral and compared the mobster to Pope Francis.
“The participation of the Casamonica family in one of the state broadcaster Rai's flagship shows is serious, and paradoxical,” he said in a statement on his Facebook page.
“Last night, more than a million viewers basically watched a replay of the mafia funeral spectacle, which had already ended up in the newspapers. This is unacceptable on a public service, especially in view of the serious risk posed by the mafia in the city and the threats that many people in Rome suffer.”
Marino said he had asked the parliamentary committee overseeing Rai to look into the incident, while deputy mayor, Marco Causi, demanded an apology from the broadcaster.
During the show, Casamonica's daughter Vera said the mafia boss was “a good father, like Pope Francis”.
His ostentatious send-off in August included a horse-drawn gilded carriage and a live band which played the theme from ‘The Godfather' film. Rose petals were also thrown from a helicopter overhead.
“I would do the same again,” she said.
Read more: Mafia boss dad was 'like Pope Francis'