The country's worst tremor in more than 80 years has also left thousands of people injured and homeless.
A telegram sent by his Secretary of State Pietro Parolin to Nepalese Catholics said: "He expresses his solidarity with all affected by this disaster and assures those who grieve for deceased family members of his closeness in prayer."
It added that Francis also "offers encouragement to the civil authorities and emergency personnel as they continue their rescue efforts and assistance to those touched by this tragedy."
Elsewhere the Church of England has released two prayers following the disaster:
O Lord our God,
Source of all goodness and love,
accept the fervent prayers of your people;
in the multitude of your mercies look with compassion
upon all who turn to you for help;
for you are gracious, O lover of souls,
and to you we give glory, Father, Son, and Holy Spirit,
now and for ever.
Amen.
Lord of all compassion
We pray for all of those caught up in the midst of tragedy or disaster.
For those who have lost life and those working to save life
For those who are worried for people they love
For those who will see their loved ones no longer
Lord Have Mercy.
For those in need of the peace that passes all understanding
For all who turn to you in the midst of turmoil
For those who cry out to you in fear and in love
Lord Have Mercy.
For those in confusion and those in despair
For those whose tears are yet to dry
For those in need of your unending love
Lord Have Mercy
Amen.