Francis, 88, went to hospital on February 14 with a severe respiratory infection that became the most serious health crisis of his 12-year papacy.
The Pope's doctors said on Saturday it would still take "a lot of time" for his ageing body to fully heal, and said they had prescribed the pontiff a further two months of rest at the Vatican.
Francis appeared on a balcony at the hospital shortly after noon on Sunday.
Using a wheelchair, as he has for several years, the Pope smiled and waved at a group of well-wishers gathered outside below.
The Pope, whose face looked swollen, appeared only for a few moments.
He spoke briefly, with a feeble voice, to thank one of the members of the crowd below, who had brought yellow flowers.
Francis had only been seen by the public once before during his hospital stay, in a photo the Vatican released last week, showing the pontiff at prayer in a hospital chapel.
In the moments before his appearance on Sunday, the crowd of hundreds of well-wishers called out for him, chanting "Francis, Francis, Francis".
The Pope has been discouraged from meeting in big groups or exerting himself, said Dr Sergio Alfieri, who co-ordinated Francis's medical team at the hospital.
"The Holy Father would have wanted to go home a few days ago, as even he realised he was improving, breathing better, and that he could work longer," Alfieri said.
"But I have to say he was an exemplary patient.
"He listened to the suggestions from me, Dr Carbone and the rest of the team."
Francis' personal doctor, Dr Luigi Carbone, said if the Pope continued his steady improvements and rehabilitation, he should eventually be able to resume all his normal activities.
Alfieri confirmed that Francis was still having trouble speaking due to the damage to his lungs and the time he spent on supplemental oxygen and ventilation.
But he said such problems were normal and predicted his voice would return.
At his home in the Santa Marta hotel, next to St Peter's Basilica, Francis will have access to supplemental oxygen and 24-hour medical care as needed, although Carbone said he hoped Francis would progressively need less and less supplemental oxygen.
"The Holy Father is improving, and we hope soon he can resume his normal activity," Carbone said.
The Argentine Pope, who has chronic lung disease, is prone to respiratory problems in winter and had part of one lung removed as a young man.
He had been admitted to hospital after a bout of bronchitis worsened.
Doctors first diagnosed a complex bacterial, viral and fungal respiratory tract infection and soon thereafter, pneumonia in both lungs.
Blood tests showed signs of anaemia, low blood platelets and the onset of kidney failure, all of which later resolved after two blood transfusions.
The most serious setbacks began when Francis experienced an acute coughing fit and inhaled vomit, requiring him to use a non-invasive mechanical ventilation mask to help him breathe.
He suffered two more respiratory crises in the following days, which required doctors to manually aspirate the mucus, at which point he began sleeping with the ventilation mask at night to help his lungs clear the accumulation of fluids.
with AP
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