Pope Francis has issued a message from his hospital bed thanking medical staff and volunteers for the “miracle of tenderness” that they offer the sick, as he continues his recovery from pneumonia.

After more than three weeks in hospital, the 88-year-old pontiff is responding well to treatment and has shown a “gradual, slight improvement” in recent days, doctors said.

For the fourth Sunday in a row, Francis did not appear for his weekly noon blessing, but the Vatican distributed the text he would have delivered if he had been well enough. In it, he thanked all those who were caring for him and others who are sick and experiencing a “night of pain”.

“Brothers and sisters, during my prolonged hospitalisation here, I too experience the thoughtfulness of service and the tenderness of care, in particular from the doctors and health care workers, whom I thank from the bottom of my heart,” read the message issued from Gemelli hospital in Rome.

“And while I am here, I think of the many people who in various ways are close to the sick, and who are for them a sign of the Lord’s presence. We need this, the ‘miracle of tenderness’ which accompanies those who are in adversity, bringing a little light into the night of pain,” he wrote.

Francis, who has chronic lung disease and had part of one lung removed as a young man, has remained in a stable condition, with no fever and good oxygen levels in his blood, for several days, doctors reported in a Vatican statement on Saturday.

The doctors said the pope’s condition testified to “a good response to therapy”. It was the first time they had reported that Francis was responding positively to the treatment for the complex lung infection that was diagnosed after he was admitted to hospital on 14 February.

But they kept his prognosis as “guarded”, meaning he was not out of danger. On Sunday morning, the Vatican reported the Francis was resting after a quiet night.

In his absence, the Vatican’s day-to-day operations continued alongside celebrations of its Holy Year, a quarter-century jubilee that brings millions of pilgrims to Rome. On Sunday, the Canadian cardinal Michael Czerny, who is close to Francis, celebrated the Holy Year mass for volunteers the pope was meant to lead.

During the mass in St Peter’s Square, the giant banner bearing Francis’s papal coat of arms fluttered from the loggia of the basilica above. Even while in hospital, the Argentinian cleric remains in charge of the Catholic church.