Pope Francis, in hospital with pneumonia, is not out of danger and will have to stay at least another week, his doctors said Friday amid questions over the 88-year-old's future as head of the Catholic Church.

Francis, who was admitted last Friday with breathing difficulties, has been slightly improving, allowing doctors to incrementally lower the amount of medication he is taking, Professor Sergio Alfieri said.

"The question is, is the pope out of danger? No, the pope is not out of danger," Alfieri told a press conference at Rome's Gemelli hospital.

"If you then ask whether he is in danger of dying at this moment, the answer is still no," he added.

What began as bronchitis developed into double pneumonia, causing widespread alarm, and fuelling speculation over Francis's ability to continue as head of the world's almost 1.4 billion Catholics.

Alfieri said "the real risk in these cases is that the germs pass into the blood", which could result in sepsis, a life-threatening condition.

Doctor Luigi Carbone said the pope, who had part of one of his lungs removed as a young man, now has a chronic lung condition and "is by definition a fragile patient".

But Alfieri stressed that "when we say that the pope is fragile, at the same time, he has incredible resilience.

"How many others would have endured all these infections with the workload he has?"

'In good spirits'

Francis, who is staying in a special papal suite on the 10th floor of the Gemelli hospital, has been moving between his bed, a chair and an adjacent chapel where he prays.

He will remain in hospital "at least for all next week", Alfieri said.

"If we send him to Santa Marta (his home at the Vatican), he'll start working again as before.

"So we're keeping him here. We're keeping him here so that when he goes back to Santa Marta, it'll be harder for him to overdo it."

Asked if the pope would be well enough to lead the Angelus prayer from his hospital window this Sunday, Alfieri said "the pope will decide".

Francis has difficulty breathing but is "in good spirits", and still has the wit of "a 70-year-old, maybe a 50-year-old", Alfieri added.

"This morning I said 'Good morning, Holy Father!' And he with a grin replied 'Good Morning Holy Son!" he said.

'Bad luck!'

But in Francis's absence from the Vatican, questions are being raised over the future of a leader with a punishing schedule who has been increasingly plagued by health issues in recent years.

"I know that some out there say my time has come, they are always bringing me bad luck!" Francis quipped to Italy's Prime Minister Giorgia Meloni when she visited him on Thursday, Italian media reported.

The Argentine is no stranger to the plotting and scheming his health woes inevitably prompt among those keen to get their man in as next pope.

After undergoing colon surgery in 2021, he joked to a group of Jesuits that "I'm still alive. Even though some wanted me dead".

"They were preparing the conclave," he said, in reference to the meeting of cardinals to elect a new pope after a death or resignation.

Francis has also undergone hernia surgery in the past four years, is overweight and suffers constant hip and knee pain, which force him to use a wheelchair most of the time.

"I love this Pope immensely", Gege Gerald, a deacon from Switzerland, told AFP in St Peter's Square, summing up the feelings of many faithful.

"I know he has done a lot of good for the Church, and he will do even more," he said.

However, Francis is also one of the oldest popes ever -- and though he has said the job is for life, the pope has left the door open to resigning like his predecessor Benedict XVI.

'Vital function'

Italian Cardinal Gianfranco Ravasi told the Corriere della Sera on Friday he did not rule out Francis stepping down.

"Francis himself has said he had already signed a letter of resignation at the beginning of his pontificate," he said.

The fact that "a fundamental vital function such as breathing" was compromised complicates the matter, Ravasi told the newspaper.

"The knee is one thing, but if one feels that the entire body is in difficulty, it's another thing."

French Cardinal Jean-Marc Aveline also said that while "completely confident in the lucidity of the pope", he would not rule out a resignation.

"If he considers that it is the best thing for the good of the Church, he will do it," he told journalists on Thursday.

But Cardinal Jean Claude Hollerich of Luxembourg said Francis certainly would not bow to pressure from his opponents to quit.

"The resignation will depend on how the pope recovers. The decision is up to Francis alone," he was quoted by the AGI news agency as saying.