Francis, who has been in Rome's Gemelli Hospital since February 14, is again receiving "non-invasive, mechanical ventilation" to help with his breathing.
"Today, the Holy Father experienced two episodes of acute respiratory insufficiency, caused by a significant accumulation of endobronchial mucus," the latest detailed medical update said.
The Pope also suffered a bronchospasm, akin to an asthma attack, which required doctors to perform two bronchoscopies, or procedures to inspect his air passages.
The Pope's prognosis remained "guarded," the statement said, which means Francis is not out of danger.
A Vatican official, who did not wish to be named because he was not authorised to discuss the Pope's health, said the pontiff's blood tests on Monday had remained stable.
The Pope's doctors believe the respiratory episode was part of his body's normal response in fighting infection, the official added.
There had been relatively upbeat statements about Francis' condition over the weekend, after a previous bronchospasm on Friday.
The Pope received ventilation after that earlier episode but switched on Sunday to receiving oxygen from a small tube placed under his nose.
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.
He has not been seen in public since entering hospital, his longest absence from view since his papacy started in March 2013, and his doctors have not said how long his treatment might last.
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