
"Something that seems ugly and scary - old age - has been on my mind for a few days," Francis said at the end of the service in the Vatican's Pauline Chapel.
Quoting from ancient Roman poets and philosophers such as Cicero and Pliny, Francis described old age as "thirst for wisdom - let's hope it will be like this for me."
"Pray for my (old age) to be like this: peaceful, religious, fruitful and also joyful," he told the cardinals.
The Vatican has opened seven email accounts to receive papal birthday messages in Latin, Italian, Spanish, Portuguese, English, French, German and Polish, but stressed that Francis was going to have a "normal" day of work engagements.
His agenda includes meetings with the Maltese president, the head of the Vatican's bishop congregation, a bishop from Switzerland and representatives of the Nomadelfia Catholic community from Tuscany.
Outgoing US President Barack Obama sent birthday wishes overnight.
"In both word and deed, Pope Francis has inspired people around the world with his message of compassion, hope and peace," Obama said in a statement.
He also thanked the pontiff for contributing to the historic rapprochement between the United States and Cuba.