Pope Francis is alert and still making jokes despite having double pneumonia, Italy's prime minister said Wednesday after visiting the 88-year-old pontiff in hospital.

Francis was admitted to Rome's Gemelli hospital with bronchitis last Friday, but the Holy See revealed on Tuesday that he had developed pneumonia in both of his lungs.

The development caused widespread alarm over the pope's health, after a series of issues in recent years, from colon and hernia surgery to problems walking.

"I was very happy to find him alert and responsive. We joked as always. He hasn't lost his proverbial sense of humour," Giorgia Meloni said in a statement after her visit.

Amid widespread speculation online, including reports of his death, the Vatican issued an early bulletin Wednesday saying he had spent a "peaceful night" in the hospital's papal suite and had breakfast.

"The pope is breathing on his own. His heart is holding up very well," a source in the Vatican added.

Francis has been speaking to friends by telephone, has been out of bed and sitting in a chair, and working on and off, the source said.

'Complex picture'

The Argentine pope, who has been head of the Catholic Church since 2013, keeps a busy schedule despite his age and ailments, and this year is busy with celebrations of the holy Jubilee year.

But he had struggled to read his homilies in the days before his hospital admission.

After an initial diagnosis of bronchitis, the Holy See revealed on Tuesday evening that "the laboratory tests, chest X-ray, and the Holy Father's clinical condition continue to present a complex picture."

A "polymicrobial infection" which has come on top of "bronchiectasis and asthmatic bronchitis, and which required the use of cortisone antibiotic therapy, makes therapeutic treatment more complex," the Vatican said.

"The follow-up chest CT scan which the Holy Father underwent this afternoon... demonstrated the onset of bilateral pneumonia, which required additional drug therapy," it added.

Bronchiectasis is when the bronchi, or air passages, thicken due to infection or another condition.

The pontiff had part of his right lung cut away when he was 21, after developing pleurisy that almost killed him.

The Vatican has cancelled a papal audience on Saturday and said the pope would not attend a mass on Sunday, although it has yet to announce plans for his weekly Angelus prayer, which is held on Sunday at midday.

'Vital energy'

Cardinal Baldassare Reina, vicar general of the Diocese of Rome, called on all parishes in the Italian capital to pray for the pope's recovery.

Candles, some with pictures of the pope on them, have been set at the bottom of a statue of Pope John Paul II outside the Gemelli hospital, where pilgrims have been coming to pray.

"I hope he recovers as soon as possible because this is the Jubilee year and he has so much to do for young people, for everyone, it's very sad," said Annamaria Santoro, an Italian woman whose son was in the same hospital.

The Vatican published drawings made by children in the hospital for Francis, as well as letters from parents asking him to pray for their sick offspring.

Jesuit theologian Antonio Spadaro, who is close to Francis, told Italy's Corriere della Sera daily the pope could be in hospital for two to three weeks.

"It is clear that the situation is delicate, but I have not perceived any form of alarmism," he said.

The pope "has an extraordinary vital energy. He is not a person who lets himself go, he is not a resigned man. And that is a very positive element, we have seen that in the past," he said.

The pope has left open the option of resigning were he to become unable to carry out his duties.

But in a memoir last year Francis said it was just a "distant possibility" that would be justified only in the event of "a serious physical impediment."