Francis, 88, had spent the afternoon alternating between resting and reading, the Vatican said in a brief statement.
His doctors have advised complete rest and Francis was unable to deliver his regular Sunday prayer to pilgrims in St Peter's Square or lead a special mass for artists held to mark the Catholic Church's jubilee year.
"I would have liked to be among you but, as you know, I am here at the Gemelli Hospital because I still need some treatment for my bronchitis," Francis said in a short written version of the prayer issued by the Vatican.
"Thank you for the affection, prayer and closeness with which you are accompanying me in these days, and I would like to thank the doctors and healthcare workers in this hospital for their care."
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.
The Vatican has said the pope would remain in hospital as long as necessary for his treatment.
Francis, who has been pontiff since 2013, has had influenza and other health problems several times over 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.
Massimo Angelelli, the head of a department at the Italian Bishops' Conference, said it might be a good thing that the pope was getting a chance to rest during a hectic year.
"During this jubilee period, his engagements have increased even more, leaving less time for recovery," he told reporters outside the hospital.
"These days, it is best that he remains, so to speak, confined to the dedicated hospital ward to fully regain his strength and receive care in a setting of complete safety — and the jubilee is still long."
The jubilee, also known as a holy year, continues until January 6, 2026.
Colombian pilgrim Patricia Afanador said she was disappointed not to see the pope at the Vatican but his health was the main concern.
"It is more important that he gets better," she told journalists in St Peter's Square.
"We carry him in our heart."
