The apology came after Pope Francis, who often contacts strangers who have written to him, called Rabuffi earlier this week to comfort him; Rabuffi suffers from an illness.
Thinking that it was a hoax, Rabuffi hung up on the Pope twice, but he finally took His Holiness seriously after the head of the Roman Catholic Church patiently rang back a third time.
"I was speechless but Francis came to my rescue, saying that what had happened was funny," Rabuffi was quoted by the Vatican newspaper as saying.
In April 2013, an Italian teenager was stunned to pick up the phone and hear the voice saying "Hello, it's Pope Francis here." Like Rabuffi, he at first thought it was a prank call but later took the Pope seriously.
In a separate development, Pope Francis called his local news kiosk in his home town of Buenos Aires to ask them to cancel his newspaper subscription; the episode took place five days after Francis was elected as the first Pope to have been born in the Americas.