The pontiff, 88, has been suffering from bronchitis for more than a week and was admitted to Rome's Gemelli hospital on Friday morning.
"To facilitate his recovery, the medical staff prescribed complete rest," said a statement released late on Saturday.
The pope's treatment on Saturday was "slightly modified based on further microbiological findings", the statement said.
"Today's laboratory tests showed an improvement in some values."
Earlier, the Vatican said the pope would remain in hospital as long as necessary for his treatment.
"We will see how he reacts to treatment," said Matteo Bruni, director of the Vatican's press office.
"I don't have a precise date (for his release)."
The later statement said Francis "did not show any fever" during the day on Saturday. It also said the pope had received Communion, a central part of Catholic worship, and had then "alternated his rest between prayer and reading".
Gemelli hospital, Rome's largest, has a special suite for treating popes, and is known especially for often treating the late Pope John Paul II during his long papacy.
Francis spent nine days at Gemelli in June 2023, when he had surgery to repair an abdominal hernia.
Outside the hospital on Saturday, groups of people were gathering under a famous statue of John Paul II to pray for Francis.
"We found out yesterday morning, with sadness," said Giovanni Di Muro, an Italian who was visiting his son in hospital.
"We hope it's nothing serious, and that everything will be fine."
Francis, who has been pontiff since 2013, has had influenza and other health problems several times over the past two years.
As a young adult he developed a case of pleurisy and had part of one of his lungs removed, and in recent times he has been prone to lung infections.
Francis has been suffering with respiratory issues since mid-December. He begged off reading statements at several of his public events in January and February, attending the occasions but asking aides to read his prepared remarks.
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