"Thanks for bringing me to the square," Francis told Massimiliano Strappetti, who was providing 24-hour care for the pontiff, the Vatican's official news outlet reported on Tuesday.
The pope, aged 88, died on Monday after suffering a stroke and cardiac arrest
The pontiff had spent 38 days in hospital earlier this year fighting pneumonia, but he returned to the Vatican almost a month ago and had seemed to be recovering.
Francis, known to push himself to exhaustion, spent his final day working, defying the advice of doctors who had told him to take two months' rest to allow his ageing body to heal.
About 35,000 Catholic faithful lined the aisles inside St. Peter's Square on Sunday as the pope made his tour, seated in a raised chair in the back of the popemobile.
There were shouts of "Viva il papa" (Long live the pope) and the vehicle stopped occasionally so Francis could bless babies brought forward by papal aides.
The rest of the pope's final Sunday was spent normally, the Vatican's outlet reported. He had a "peaceful dinner," it said. The first signs of a "sudden illness" occurred at 5.30am on Monday.
"A little more than an hour later, making a farewell gesture with his hand to Strappetti ... the pontiff went into a coma," said the outlet.
"He did not suffer, and it all happened very fast."
The pontiff will lie in state inside his coffin from Wednesday through Friday.
Francis' funeral will take place on Saturday at the Basilica of Saint Mary Major in Rome, the Vatican also announced on Tuesday, as the Church prepares to lay him to rest and start the process of deciding on a new pontiff.
Before he died, Francis expressed his desire to be buried at the basilica, one of his favourite places, and not in the grander St Peter's Basilica in the Vatican as is customary for deceased popes.
Francis' body is currently lying in an open coffin in the chapel of the Santa Marta guesthouse, his former residence, where cardinals, officials and employees of the Vatican are able to bid farewell to him.
Members of the Swiss Guard - a corps of Swiss soldiers responsible for the safety of the pontiff - are stand guard over the pontiff's body.
A large church service in the Vatican will precede the burial at Saint Mary Major.
As spiritual leader of the world's 1.4 billion Catholics, Jorge Mario Bergoglio was the first pontiff from Latin America, the first Jesuit, and the first to be named after St Francis of Assisi, a medieval monk who lived in poverty.
In the coming weeks, the Church will hold a closed meeting of cardinals, called a conclave, at the Vatican in order to decide on who will be Francis' successor.
with DPA
