While the Pope did not appear from the 10th-floor suite of windows, he acknowledged their presence in the traditional Sunday blessing.
"I know that many children are praying for me; some of them came here today to Gemelli as a sign of closeness,'' the pontiff said in the Angelus text prepared for the traditional prayer but not delivered live again.
"Thank you, dearest children! The Pope loves you and is always waiting to meet you,'' Francis said.
The Reverend Fortunato, the president of the pontifical committee for World Children's Day who organised the event, said that the gathering of children with their parents was a form of spiritual medicine for the 88-year-old pontiff. He called it ''the most beautiful caress.''
"The children represent a symbolic medicine for Pope Francis,'' Fortunato said.
''Letting him know that so many children are here for him cheers the heart.''
A small group of the children, whose balloons represented the colours of the Vatican flag, briefly entered the hospital to leave behind their drawings, messages and flowers for Francis.
Many of the children came from poorer Italian districts or from countries impacted by war, some having arrived in Italy from Afghanistan and Syria via humanitarian corridors set up by the Sant'Egidio charity in agreement with the Italian government; others were from Ukraine, Gaza, South America and Africa.
One of them was 12-year-old Anastasia, who got up at 5am local time to make the trip from Naples with the hopes of delivering the message directly to the Pope.
"I wrote, 'Pope Francis, get well and return home soon,'" she said.
"'We love you, all of the children are praying for you.'"
Francis typically delivers the Angelus from a window overlooking St Peter's Square to the gathered faithful, who have grown more numerous due to the Jubilee year that Francis inaugurated in December.
In the written text, Francis said he was thinking of others, who like him, are in a fragile state.
"Our bodies are weak, but even like this, nothing can prevent us from loving, praying, giving ourselves, being for each other, in faith, shining signs of hope,'' the Pope said.
The Pope no longer in critical condition
Along with a stop at St Peter's to seek indulgences by walking through the basilica's Holy Door, pilgrims are now also adding a stop at Gemelli, a 15-minute train ride from the Vatican.
Doctors this week said the pontiff was no longer in critical, life-threatening condition, but they have continued to emphasise that his condition remained complex due to his age, lack of mobility and the loss of part of a lung as a young man.
Still, they are issuing fewer medical bulletins as the pontiff has been on an upward trajectory. An X-ray this week confirmed that the infection was clearing.
Francis has not been seen publicly since he was admitted to the hospital February 14 after a bout of bronchitis that made it difficult for him to speak. Doctors soon added a diagnosis of double pneumonia and a polymicrobial (bacterial, viral and fungal) infection.
The first three weeks of his hospitalisation were marked by a rollercoaster of setbacks, including respiratory crises, mild kidney failure and a severe coughing fit.
Doctors in the most recent medical update on Saturday said they were working to reduce the Pope's nighttime reliance on the non-invasive ventilation mask, which will allow his lungs to work more.
Doctors underlined that while the Pope's condition is stable, he still requires hospitalisation for treatment along with physical and respiratory therapy, which are "showing further gradual improvements," the Vatican said Saturday in the first medical update in three days.
The next update won't be issued until the middle of next week, the Vatican said.
