His latest blood tests and scans reveal the inflammation in his lungs is easing.
"The clinical conditions of the Holy Father are stable," said a brief Vatican statement on Wednesday.
The 88-year-old's been in hospital for six days now, and there are reports that the Swiss Guard has been rehearsing his funeral.
But Italy's PM says he was alert and responsive when she visited him yesterday. She said, "He hasn't lost his proverbial sense of humour."
The Vatican's official media outlet reported that messages of support for Francis have come in from around the world. Pilgrims at the Vatican on Wednesday for the Pope's cancelled weekly audience expressed hope for his recovery.
"We will pray for him so that he can recover as soon as possible," said Gianfranco Rizzo, a pilgrim from Bari, Italy.
