Vatican City - Pope Francis remains stable after almost four weeks in the hospital with pneumonia, the Vatican said on Tuesday, declining to speculate on when he might go home, the day after doctors indicated he was no longer in danger.

The 88-year-old head of the world Catholic Church has been in Rome's Gemelli hospital since February 14 with pneumonia in both lungs, suffering several respiratory crises that sparked real fear for his life.

But on Tuesday evening – a day after indicating that he was out of imminent danger – the Holy See said that the pope's condition continued to be stable.

"It is clear that the situation remains stable... and with these slight improvements within a framework for doctors that remains complex," the Vatican said.

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On Monday, following a week of steady improvements in Francis's condition, the Vatican said his prognosis was no longer considered "reserved", or uncertain, meaning his life is no longer at imminent risk.

But his condition remained complex and he would require hospital treatment for "several more days", it said on Monday – with the implication that afterwards, he could go home to the Vatican.

A Vatican source on Monday said that Francis still had pneumonia but confirmed there was "no imminent danger" to his life.

Despite the improving scenario, the Vatican on Tuesday said that it was still unknown when exactly Francis might be released from the hospital.

The source denied reports that preparations were under way for Francis's return to the Santa Marta residence.

Francis missed the start of the Lent religious period last week but there are hopes he might be able to participate in celebrations for Easter, the holiest period in the Christian calendar, which culminates on April 20.