The pontiff, 88, has been suffering from bronchitis for more than a week and was admitted to Rome's Gemelli hospital on Friday morning.
The Vatican said on Saturday the Pope would remain in hospital for as long as his treatment required.
His doctors have advised complete rest, and Francis was unable to deliver his regular weekly prayer on Sunday to pilgrims in St Peter's Square or lead a special mass for artists to mark the Catholic Church's Jubilee Year.
The Vatican on Sunday described his condition as "stable" and said his treatment was ongoing. It said earlier he would remain in hospital for as long as required.
While in hospital over the weekend, the Pope continued his recent practice of making phone calls to speak with members of a Catholic parish in Gaza, Italian broadcaster Mediaset reported on Monday.
One of the parish members said Francis had called on both Friday and Saturday and was in "good humour" but sounded "a bit tired".
He has also cancelled a visit to Rome's Cinecitta film studios, scheduled for Monday.
"Thank you for the affection, prayer and closeness with which you accompany me in these days," Pope Francis wrote on X on Sunday.
The cardinal who led mass on Sunday in the absence of Francis opened the service with a message of support.
"Our first thought goes to Pope Francis. We pray for his health, offering thanks for the vision and support that he always gives us," Cardinal Jose Tolentino de Mendonca said during the mass in St Peter's Basilica.
Francis, who has been pontiff since 2013, has had influenza and other health problems several times in the past two years.
As a young adult, he developed a case of pleurisy and had part of one of his lungs removed, and in recent times he has been prone to lung infections.
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