The pontiff's feelings were expressed in a telegram sent by his Secretary of State Pietro Parolin to the Nepalese Catholic authorities.
"He expresses his solidarity with all affected by this disaster and assures those who grieve for deceased family members of his closeness in prayer," the statement read.
The pontiff also "offers encouragement to the civil authorities and emergency personnel as they continue their rescue efforts and assistance to those touched by this tragedy."
Dozens more people were reported killed in neighbouring India and China and there are fears the final toll could be much higher.