Francis, 88, has been in Rome's Gemelli hospital for more than three weeks with a severe respiratory infection that has required continuously evolving treatment.
"The clinical condition of the Holy Father in recent days has remained stable and, consequently, indicates a good response to the treatment," the latest detailed medical update said.
The Pope, it said, has continued to have no fever and his blood test have remained stable.
Although the doctors said they had seen "a gradual, slight improvement" in the Pope's overall condition, they maintained a guarded prognosis "in order to ensure these initial improvements continue in the coming days".
Francis 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.
Doctors not involved in Francis' care have said the Pope is likely to face a long, fraught road to recovery, given his age and other long-standing medical conditions.
The tone of the updates from the Vatican has been cautiously upbeat in recent days, after the Pope suffered what was described as two episodes of "acute respiratory insufficiency" on March 3.
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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