The 86-year-old pontiff left Rome's Gemelli hospital in a wheelchair, smiling and waving to reporters and well-wishers at the main entrance as he was taken to a waiting car.

"The pope is well. He is in better shape than before," Sergio Alfieri, who operated on Francis on June 7, told reporters.

The Vatican said he would recite his noon prayer on Sunday in St. Peter's Square and resume private audiences next week but would skip the Wednesday general audience in the square "to safeguard his post-operative recovery".

Francis is due to receive Cuban President Miguel Mario Díaz-Canel on Tuesday, diplomatic sources have told Reuters.

As he was being taken to the car, Francis was asked about the latest migrant tragedy off the coast of Greece, where at least 79 people drowned early on Wednesday and hundreds more were missing and feared dead.

"So much pain, so much," Italian media quoted him as saying.

Before returning to the Vatican, Francis stopped to pray at an icon of the Madonna at the Basilica of Santa Maria Maggiore, one of his custums when he returns from a trip or a hospital stay.

When he reached a Vatican gate he briefly got out of his car, and, standing for a minute, individually thanked members of the Italian police escort.

Alfieri said the pope was well enough to travel. Francis travels to Portugal at the start of August and Mongolia at the end of that month.

"He will be able (to carry out his duties) better than before because he no longer will have the discomfort. He will be a stronger pope," Alfieri said.

"He already has resumed working. We asked him to rest a bit and I am certain that this time he will listen to us a bit more because he has some important commitments, which he told us he would respect."

"The pope told us 'Thank you, pray for me, I am still alive'," Alfieri said.

The pope traditionally takes all of July off, with the Sunday blessings his only public appearances, so he will have next month to rest before his trips.