The 88-year-old pope was admitted to Rome's Gemelli hospital on February 14 with a severe respiratory infection that has required continuously evolving treatment.
In a relatively upbeat health bulletin on Wednesday, the Vatican said the pope had carried out some work and had spent much of the day in an armchair. The last time the Vatican specified that the pope had been able to work was on February 27.
However, his doctors reiterated that his prognosis was "guarded", meaning he was not yet out of danger.
The Vatican also said that Francis would once again be reconnected to non-invasive mechanical ventilation overnight after it was removed during the day, underscoring his continued difficulty in shaking off the dangerous illness.
When he is not on mechanical ventilation, which pushes air into the lungs and does not require a patient to be sedated, the pope receives a high-flow of oxygen via a small nasal hose under his nose.
For the first time since February 24, the Vatican said the pope had made a call to the Catholic parish in Gaza, which he has done frequently during the Israel-Hamas war.
Francis suffered what the Vatican described as two episodes of "acute respiratory insufficiency" on Monday, but has had no repeat of this since then.
He has not been seen in public since entering hospital, his longest such absence since his papacy started 12 years ago. His doctors have not said how long the treatment might last.
His illness has meant that he has already missed a number of Church events, including a service on Wednesday known as Ash Wednesday, which marks the start of a 40-day period leading to Easter Sunday and which he normally presides over.
Instead, Cardinal Angelo De Donatis stood in for him.
"We feel deeply united with him at this time," De Donatis told the congregation in a Rome church.
"We thank him for offering his prayers and his sufferings for the good of the entire Church and the whole world."
Christians receive a sign of the cross in ashes on their forehead during the service - a rite intended to remind people of their mortality. Donatis dwelt on the theme in his sermon.
"In many ways, we try to banish death from our societies ... Death, however, imposes itself as a reality with which we have to reckon, a sign of the precariousness and brevity of our lives," he said, in the homily which had been originally prepared for Francis to deliver.
The Vatican said the pope had also taken part in an Ash Wednesday service in his hospital suite.
Francis has experienced several bouts of ill health over the last two years and is prone to lung infections because he had pleurisy as a young adult and had part of one lung removed.
Double pneumonia is a serious infection in both lungs that can inflame and scar them, making it difficult to breathe.
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