Pontiff enters his fourth week in hospital in Rome.

Pope Francis, battling double pneumonia in Rome's Gemelli Hospital, remains in a stable condition and has shown a good response to therapy, the Vatican said on Saturday night.

The clinical condition of the 88-year-old pontiff indicates "a gradual, slight improvement" however doctors stress that his prognosis remains "guarded", according to the latest health update.

Noting that Francis "has been without a fever at all times", the Vatican said the pope had spent Sunday alternating between rest, prayer and work.

On Thursday evening a surprise audio message from the pontiff was played at a Rosary in St Peter's Square, in which a breathless, weak-sounding Holy Father thanked everyone for their prayers, in what was his first public sign of life in three weeks.

As Francis enters his fourth week in hospital, public prayer vigils are being held every night at St Peter's, amid continuing uncertainty and concerns over the pope's health.

Image: Pope Francis balloons outside the Gemelli Hospital. Photo Wanted in Rome.