The Daily Mail has reported that Franco Rabuffi hung up after the Pope called to comfort him when he was ill.
The pontiff often contacts strangers who write to him or whose problems he hears about, and contacted Mr Rabuffi on Monday to speak with him.
The man disconnected the call twice, thinking it was a hoax. He later apologised personally, and it has been reported that Pope Francis found the incident very amusing.
The third time the Pope rang Mr Rabuffi took him seriously, according to the Vatican newspaper l'Osservatore Romano.
He said: "I was speechless but Francis came to my rescue, saying that what had happened was funny."
Mr Rabuffi, along with his wife, appeared before the pope during the Vatican's general audience on Wednesday and personally apologised for his mistake.
