Francis, 88, had suffered two episodes of what the Vatican described as "acute respiratory insufficiency" on Monday.
The latest detailed medical update on his condition said the Pope had suffered no similar problems on Tuesday.
"Throughout the day, the Holy Father's clinical condition has remained stable," it said.
"He has remained without fever, always alert, collaborating with his treatment, and well-oriented."
Francis has been in Rome's Gemelli hospital for more than two weeks.
He was admitted on February 14 with a severe respiratory infection that triggered other complications.
The bulletin was the second cautiously upbeat report of the day, after the Vatican press office said earlier that the Pope's condition had stabilised overnight on Monday.
While the Pope had stopped using non-invasive mechanical ventilation to help him breathe during the day on Tuesday, the latest update said he would return to using ventilation overnight on Tuesday.
Doctors said his prognosis as "guarded," meaning the Pope is not out of danger.
Francis has not been seen in public since entering hospital, his longest absence from view since his papacy started in March 2013.
His doctors have not said how long his treatment might last.
The Pope's public absence has stoked speculation, even from senior cardinals, that he could choose to follow in the footsteps of his predecessor Benedict XVI and resign the papacy.
But biographers and friends of the pontiff describe him as a "fighter" with no plans to resign.
Monday's setback followed two days of relatively upbeat statements about his condition.
The Vatican said the two respiratory episodes on Monday were caused by "a significant accumulation of endobronchial mucus".
The Pope, it said, had suffered a bronchospasm, akin to an asthma attack, and had required two bronchoscopies, or procedures to inspect his air passages.
A Vatican official, who did not wish to be named because he was not authorised to discuss the Pope's health, said on Tuesday that the Pope's doctors believe the respiratory episodes have been part of his body's normal response in fighting infection.
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.
24°C