ROME (AP) — Pope Francis woke up Tuesday to good news from his doctors: They upgraded his prognosis and say he is no longer in imminent danger of death as a result of the double pneumonia that has kept him hospitalized for nearly a month in the longest and gravest threat to his 12-year papacy.

The 88-year-old pope isn’t out of the woods yet, however. Doctors are still cautious and have decided to keep him hospitalized for several more days to receive treatment, not to mention a period of rehabilitation he will likely need.

But the doctors said he remains stable and has consolidated improvements in recent days, according to blood tests and his good response to treatment. Francis, who has chronic lung disease, is still using supplemental oxygen during the day and a ventilation mask at night to help him breathe.

In an early update Tuesday, the Vatican said Francis woke up around 8 a.m. after a quiet night. The Argentine Jesuit has regularly been sleeping in while at Gemelli hospital; his usual wakeup time at the Vatican is around 4:30 a.m.

Late Monday, doctors lifted their “guarded” prognosis for the pope, meaning they determined he was no longer in imminent danger as a result of the original respiratory infection he arrived with on Feb. 14. But their caution remained, given Francis’ fragility and risks of other complications.

“In view of the complexity of the clinical picture and the important infectious picture presented on admission, it will be necessary to continue medical drug therapy in a hospital setting for additional days,” the Vatican statement said.

In a sign of his improved health, Francis followed the Vatican’s weeklong spiritual retreat via videoconference on Monday in both the morning and afternoon sessions, something he was likely to continue to do through the week.

This week also counts some important anniversaries for Francis: Tuesday was the 67th anniversary of his entry into the Jesuit religious order’s novitiate, and Thursday marks the 12th anniversary of his election as pope.

Francis, who had part of one lung removed as a young man, had what was just a bad case of bronchitis when he was hospitalized last month. The infection progressed into a complex respiratory tract infection and double pneumonia that has raised questions about the future of his pontificate.

He was still keeping his eye on things, however. The Vatican said he had been informed about the floods in his native Argentina, sent a telegram of condolences and expressed his closeness to the affected population. In addition, a Vatican cardinal close to Francis spoke out Monday to deny some negative media reports that have circulated in his absence.

The Vatican development office released a letter written by Cardinal Michael Czerny to one of Francis’ close friends, the Argentine social justice activist Juan Grabois. Grabois had traveled to Rome to pray for Francis at Gemelli hospital, and some Italian media reported that he had tried to forcibly get into Francis’ 10th floor hospital suite, a claim he denied.

In the March 6 letter, Czerny told Grabois that Francis “knew of your presence in Rome and your daily vigils of prayer and spiritual solidarity at Gemelli Polyclinic and I’m sure this gave him a true comfort and support.”

“Additionally, I know that you join me in strongly repudiating the unfounded versions that have circulated in some media about alleged inappropriate behavior in the hospital,” Czerny wrote.

The Vatican is always abuzz with rumor but has gone into overdrive with speculation about Francis’ health and talk of conclaves, even though Francis is very much alive and in charge. The fact that Czerny felt it necessary to defend one of Francis’ friends suggested that the rumor and maneuvering in Francis’ absence had crossed a line.