Pope Francis's heart is holding up very well despite his pneumonia, a Vatican source said on Wednesday, amid growing concerns over the hospitalised 88-year-old's condition.

The pontiff was admitted to a Rome hospital with bronchitis last week after suffering breathing difficulties, but the Holy See revealed on Tuesday evening that he had developed pneumonia in both of his lungs.

"The pope spent a peaceful night, woke up and had breakfast," the Vatican said on Wednesday after Francis's fifth night at the Gemelli hospital, which has a suite reserved especially for popes.

"The pope is breathing on his own. His heart is holding up very well," a source in the Vatican said.

Francis has been speaking to friends by telephone, has been out of bed and sitting in a chair, and working on and off, the source said.

On Tuesday, the Vatican had reported that Francis was in "good spirits."

But in an evening medical bulletin, it warned that "the laboratory tests, chest X-ray, and the Holy Father's clinical condition continue to present a complex picture."

A "polymicrobial infection" which has come on top of "bronchiectasis and asthmatic bronchitis, and which required the use of cortisone antibiotic therapy, makes therapeutic treatment more complex," the Vatican said.

"The follow-up chest CT scan which the Holy Father underwent this afternoon... demonstrated the onset of bilateral pneumonia, which required additional drug therapy," it added.

The pontiff had part of his right lung cut away when he was 21, after developing pleurisy that almost killed him.

The Vatican has cancelled a papal audience on Saturday and said the pope would not attend mass on Sunday, although it has yet to announce plans for his weekly Angelus prayer, which is held on Sunday at midday. (AFP)