Pope Francis, battling pneumonia in both lungs, slept well and is resting, the Vatican said Thursday, after revealing the 88-year-old's condition was slightly improving.

Nevertheless, both the Vatican and experts warned the pontiff was not out of danger.

Francis, who had part of a lung removed as a young man, was admitted to Rome's Gemelli hospital on 14 February, initially with breathing difficulties.

But his condition subsequently deteriorated, sparking fears that the head of the world's nearly 1.4 billion Catholics might not pull through.

"The Pope slept well last night and is now resting," the Vatican said in a morning bulletin, fuelling hope the Argentine might be rounding a corner.

A Vatican source said the pope also "got up and had breakfast."

"The clinical conditions of the Holy Father in the last 24 hours have shown a further, slight improvement," the Vatican said late Wednesday.

But it warned, "Although a slight improvement is being recorded, the prognosis remains reserved."

Respiratory attacks Francis suffered at the weekend that required high levels of oxygen and blood transfusions have not repeated, although he continues to receive oxygen and do breathing exercises.

On Wednesday, the Vatican said a CT scan performed Tuesday showed "normal progression of the pulmonary inflammatory condition" while blood tests on Wednesday confirmed the improvement. 

It also said that a mild renal insufficiency detected at the weekend "had resolved."

As Catholics across the globe pray for Francis, doctors have warned the path to recovery could be long, with the Jesuit pontiff likely staying in hospital beyond this week.

'Not there yet'

Francesco Blasi, head of pneumology at Milan Polyclinic, and Stefania Vaglio, director of the Immune-haematology unit at the Sant'Andrea Polyclinic in Rome, said the pope's prognosis remains reserved because "the respiratory problem has not been resolved."

"For an 88-year-old who was already suffering from a chronic respiratory disease before the pneumonia, (his condition) remains critical at least until the improvement is defined as stable," they said in a joint interview with the Corriere della Sera daily.

"We are not there yet. More days of waiting are needed." 

The current hospitalisation is Francis's longest, at 14 days so far.

Pilgrims and faithful have been flocking to the Vatican and the Gemelli to pray for Francis, with another prayer service to be held in St Peter's Square later Thursday evening.

Despite his critical condition, Francis has kept up with Church matters from his hospital suite.

"The Pope wants to push through decisions he cares about, it is a manifestation of strength, of a willingness to govern," Adriano Prosperi, a historian specialised in the Church, told the Repubblica daily.

The Argentine, elected in 2013, has aroused both fervour and fury within the Church with reforms aimed at opening the doors of a centuries-old institution to the modern-day faithful.

"Francis knows that what he leaves behind is in danger, and wants to protect it," Prosperi said.