After lunch with President Giorgio Napolitano in the Quirinale palace, the Queen crossed the Tiber for a private audience with the Pope, who gave her a blue orb decorated with a silver cross for her eight-month-old great grandson.
“It’s for the little boy,” the Pope said in his native Spanish, as he pointed to the orb - a traditional emblem of the power of Christian monarchs.
For centuries, royal dynasties have used orbs to represent their dominion, while the cross on top of it symbolises their Christian faith - a fitting gift for a child who will one day be King and Defender of the Faith.
It sat on a silver base on which was inscribed, in English, the words: “Pope Francis to His Royal Highness Prince George of Cambridge”.
“That’s very nice, he will be thrilled,” said the Queen, who wore a lilac coat over a lilac and green chiffon dress and a matching lilac hat.
Then, perhaps realising that a heavy sphere topped by a cross with four sharp points was not entirely suitable for a baby, she added: “When he’s a little older.”
The orb Pope Francis gave the Queen (GETTY IMAGES)
In return, the Queen and the Duke of Edinburgh gave Pope Francis a hamper of food and drink produced on the royal estates of Windsor, Sandringham and Balmoral, along with honey produced in the gardens of Buckingham Palace.
As the Duke held up a bottle of malt whisky, the Queen said: “It’s from Balmoral, up in Scotland,” to which the Pope looked slightly taken aback before smiling.
The hamper also included Coronation Best Bitter and a haunch of venison from Windsor Castle, cider, quince jelly and “Granddad’s chutney”, from Sandringham and shortbread from Balmoral. It was “for you personally”, the Queen told the Pontiff.
But a Vatican spokesman said the Pope would probably donate it to a charity for the poor in Rome, in keeping with his message of compassion for those most marginalised in society.
It was the first meeting of the Queen and Prince Philip with Pope Francis, 77, since he was elected pontiff last March. As they swept into the inner sanctum of the Vatican they were met by an honour guard of a dozen Swiss Guards in traditional striped red, blue and yellow uniforms.
“Sorry to keep you waiting. We were having a very pleasant lunch with the president,” the Queen, 87, told Pope Francis as she arrived more than 20 minutes late, after having a meal with Giorgio Napolitano, Italy’s 88-year-old president.
After a brief introduction, the three had a private meeting which lasted 17 minutes. Neither the Vatican nor Buckingham Palace would reveal details of what they discussed but as respective heads of the Anglican Church and the Catholic Church, ecclesiastical matters were almost certainly touched on.
The Argentine Pope gave the Queen herself a high-quality copy of a parchment decree from 1679, in which the Holy See declared that King Edward the Confessor, the 11th century monarch, should be made a saint of “the Universal Church” rather than be regarded as solely an English saint.
The decree was issued by Pope Innocent XI in response to an appeal by the Howards, the powerful English Catholic family.
“It’s an ecumenical message - we have the same traditions, many of the same saints,” said Father Federico Lombardi, the Vatican spokesman. “King Edward is a saint for the Catholic Church as well as for the Anglicans.”
Through a translator Pope Francis explained in Spanish that King Edward, who is buried in Westminster Abbey, had been made a saint in 1161, nearly a century after his death.
“Oh he was canonised was he?” the Duke of Edinburgh exclaimed, while the Queen thanked the pontiff: “That’s very kind, how very interesting.”
Pope Francis also had a gift for the 92-year-old Duke - a set of papal medallions in gold, silver and bronze. “It’s the only gold medal I’ve ever won!” the Duke joked.
There was more light-heartedness when the Queen gave the Pope a set of framed, signed photographs of herself and her husband. “I’m afraid you have to have a photograph, it’s inevitable,” she said.
During the visit the Royals exchanged gifts with Pope Francis (REUTERS)
As the Queen and Prince Philip flew from Rome’s Ciampino airport back to Britain after a visit lasting just five hours, it emerged that Italy can soon expect another royal visit - Prince Harry is due to attend the 70th anniversary commemoration of the bloody Battle of Monte Cassino next month.
It was the Queen's first visit to Rome in 14 years. She was welcomed to the Italian capital by an honour guard of Sardinian grenadiers, Carabinieri cavalry, navy and air force, and given a bouquet of flowers by an eight-year-old girl.
She was later pictured chatting to Mr Napolitano, 87, with whom she is said to have a friendly relationship.
The visit to the Vatican was agreed amid assurances that the Holy See would remain neutral on the contentious issue of the Falkland Islands.
The Pope recently had a lengthy meeting with Cristina Kirchner, the president of Argentina, who has called on her countryman to intercede in the dispute with the UK over the British territory in the South Atlantic.
Officials would not say whether the Queen and Pope Francis would discuss the islands but Nigel Baker, the British ambassador to the Holy See, said the Vatican had restated its neutral position on the dispute.
"The Vatican has been clear with us, including in the last week and at a very senior level, that their long-standing position of neutrality on this issue remains in force," he said.
As archbishop of Buenos Aires, the then Cardinal Jorge Mario Bergoglio backed calls for the islands to be ceded to Argentina.
Two years ago he said that the Argentinean soldiers who died in the war had been trying to "defend the homeland, to reclaim what is theirs" and that Britain had "usurped" the islands.
The South American pontiff also recently met a group of 12 Argentine veterans of the 1982 war, who came to the Vatican holding banners calling for "peace in the South Atlantic".
That message accords with the position of the Argentine government, which argues that Britain is in breach of what it says should be a demilitarised zone around the Falklands.
It was the Queen's seventh encounter with a pontiff. She previously met Pius XII in 1951, John XXIII in 1961, John Paul II in 1980, 1982 and 2000, and Benedict XVI during his visit to the UK in 2010. Five of those encounters took place in Rome.
The meeting came during the centenary of Britain re-establishing relations with the Holy See in 1914, centuries after the schism caused by Henry VIII's divorce.