The Argentinian pontiff was handed the sign on Wednesday during his weekly walkabout in St Peter's square. The Spanish text read: "The time has come for dialogue between Argentina and the United Kingdom on the Malvinas" - using the Spanish term for the Falklands.
A Vatican spokesman suggested that the Argentinian pope may not even have been aware of what was written on the placard.
"It happened during a general audience when many believers present the pope with all sorts of objects, often to have a photograph taken," said spokesman Ciro Benedettini.
After the photo went viral, Francis felt the need to explain that, while he admired the priest, he did not share his revolutionary views.
Britain rejects Argentina's requests for dialogue over the long-term future of the Falklands, insisting there is nothing to discuss since 99.8 percent of the islanders voted in a 2013 referendum to remain a British overseas territory.
Argentina claims it inherited the remote islands from Spain when it gained independence and the stakes involved have increased in recent years with the discovery of significant exploitable oil and gas reserves around the remote islands.
