Pope Francis participated remotely in the Vatican’s spiritual retreat Tuesday after getting 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 was resuming his physical and respiratory physiotherapy after a quiet night. In a sign of his improved health, Francis also followed the Vatican’s weeklong spiritual retreat via videoconference for a third day, and spent some time in prayer in his private chapel, the Vatican said.

“It really makes me happy, because we were sad as it looked like he was not recovering,” said Sister Maria Letizia Salazar, a nun who was praying for Francis on Tuesday outside the Gemelli hospital. “But now that I’ve got this news I am very happy.”

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

Doctors on Monday 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, the severity of the original infection and overall complexity of his condition.

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.