Msgr. Lucio Vallejo Balda was found guilty on July 7 of stealing and passing on documents to Italian journalists Gianluigi Nuzzi and Emiliano Fittipaldi.
Pope Francis and Zuckerberg spoke about "how communications technology can be used to alleviate poverty, encourage a culture of encounter and help deliver a message of hope."
"To the extent that the difficulties seem more insurmountable and the prospects of security and peace seem more unclear, our prayer should be more insistent," he said.