The 88-year-old Pope was spending his 12th night at Rome's Gemelli hospital, the longest hospital stay of his papacy.
"The clinical conditions of the Holy Father remain critical, but stable," the latest forthright health update read.
The Pope's prognosis, it said, remains "guarded".
But his hemodynamic parameters, a measure of the functioning of his body's circulatory system, were also "stable".
A Vatican official, who did not wish to be named because he was not authorised to discuss the Pope's condition, said earlier on Tuesday that Francis was eating normally, moving about his hospital room and continuing his treatment.
The Vatican also revealed that Francis had met his second-in-line, Cardinal Pietro Parolin, and Parolin's deputy on Monday.
It said they had discussed several pending cases for sainthood.
In addition, the Vatican announced new appointments that would have needed the Pope's approval.
Francis has been working occasionally from the hospital as Vatican business continues apace during his illness.
The Pope's only other known VIP visitor was Italian Prime Minister Giorgia Meloni, who saw him on February 19.
On Monday, the Vatican said the pontiff's condition remained critical but had shown a "slight improvement," adding that a "mild kidney insufficiency," first reported at the weekend, was not a cause for concern.
Tuesday's statement did not mention renal issues.
Double pneumonia is a serious infection of both lungs that can inflame and scar them, making it difficult to breathe.
The Vatican has said the Pope's infection is "complex" and caused by two or more microorganisms.
Francis, who has been pontiff since 2013, has suffered several bouts of ill health over the past two years.
He is prone to lung infections because he developed pleurisy as a young adult and had part of one lung removed.
Thousands of people gathered in St Peter's Square on Monday evening to pray for his recovery.
His friend, the Honduran cardinal Oscar Rodriguez Maradiaga, told Italy's la Repubblica newspaper: "I think ... it's not time for him to go to heaven yet."
The Pope signalled in early February that he had a bad cold, which meant he could not read out his speeches.
Despite this, he continued to have meetings every day and even take part in open-air Masses, despite the chill.
Some well-wishers have said he should have taken better care of himself but Maradiaga defended Francis' work ethic.
"He is aware that he has a mission he must carry out, and nothing stops him. The Pope explained that he did not accept his election (as pontiff) in order to rest," he said.
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