In an early update on Wednesday, the Vatican said Francis spent his fifth night in Rome's Gemelli hospital peacefully.
"He had a tranquil night, woke up and had breakfast," spokesman Matteo Bruni said.
The pope, who had the upper lobe of his right lung removed as a young man, was in good spirits and grateful for the prayers for his recovery, Bruni said.
On Wednesday, Francis' vicar for Rome urged all the faithful to devote an hour of silent prayer for the pope before evening vespers services, and pilgrims who had planned to attend his weekly general audience came to St Peter's Square anyway to offer a prayer after it was cancelled.
"I think many people are disappointed but I think more importantly we really have to pray for his health," said Sister Charlene, a nun from Singapore who was in the piazza.
Francis was admitted to the Gemelli hospital Friday after a week-long bout of bronchitis worsened.
On Monday, medical personnel determined that he was suffering from a polymicrobial respiratory tract infection, meaning a mix of viruses, bacteria and possibly other organisms had colonised in his respiratory tract.
Late Tuesday, the Vatican said a chest CT scan showed the onset of bilateral pneumonia on top of asthmatic bronchitis, which is being treated with cortisone and antibiotics.
Bronchitis can lead to pneumonia, which is a deeper and far more serious infection of the lungs' air sacs.
Pneumonia can develop in part or all of one lung or in both lungs. It tends to be more serious when both lungs are affected because there isn't healthy tissue to compensate.
Treatment varies by severity but can include providing oxygen through a nasal tube or mask, intravenous fluids — and treatment of the underlying cause of the infection.
To date, Francis is breathing on his own and his heart function is said to be good.
He has eaten breakfast every day, gotten out of bed, read the newspapers and done some work from his hospital room.
"Pope Francis is a strong man who does not let difficulties get him down," said the Rev. Enzo Fortunato, who heads a new Vatican committee on children.
The fact that Francis is keeping up with his ordinary routine, including receiving the Eucharist, "is a sign of a man who wants to experience the ordinariness of illness in the hospital".
The Vatican hasn't provided any information about how Francis is responding to any of the drugs he has been given other than to say he isn't running a fever.
The Argentine pope, who has previously admitted to being a non-compliant patient, has a number of conditions that make him particularly at risk for complications.
Aside from his age, he is not physically active and uses a wheelchair, limiting his ability to clear the fluids building up in his lungs.
Severe cases of pneumonia are typically treated for about one to two weeks, but recovery in an older person could extend beyond that.
Despite the less than positive news about Francis' condition, Francis was receiving get-well drawings and cards from children being treated in the hospital's oncology ward.
And at the Vatican on Wednesday, Holy Year pilgrimages continued, with groups of faithful walking through the Holy Door of St Peter's Basilica on a chilly and cloudy day.
"We are very happy to be here but we are also sad for the pope's sickness," said Amparo Alcala', who was leading a large group of pilgrims from Valencia, Spain.
"He is doing great things, most of all for the women in the church, and this gives us a lot of joy. We are praying for his recovery and that he might come back, if this is God's will."
A group of South Korean pilgrims in traditional costumes had planned to attend Francis' weekly Wednesday general audience and show off their national dress, as pilgrims often do for the pope's weekly appointment.
When it was cancelled, they came anyway.
"The Lunar New Year was very recent so we also wanted to bow traditionally and formally in front of him," said Junhee Christina Kim, a pilgrim from Seoul, South Korea.
