Cristina Fernandez tweeted a photo of the Pope, the former archbishop of Buenos Aires, holding the sign, which is part of a campaign marking the 50th anniversary of a United Nations resolution calling for the two countries to hold talks over the dispute.
The Pope swiftly quashed the attempt to link him to the cause after his spokesman said the small poster was handed over during a weekly public gathering when lots of people give him things and that he had no idea what the item was.
The Holy Father did not even realise he had this object in his hands. He has discovered this just now after seeing the photograph, Father Ciro Benedettini said in a phone interview on Wednesday. The picture was taken during the general audience when many people give items to the Holy Father.
The Argentine president has persistently lobbied the Pope to intervene on her country's behalf but the Vatican has been clear it doesn't wish to involve itself in the dispute.
Tensions between the two countries culminated in war in 1982 after Argentine forces invaded the Falkland Islands. More recently, the discovery of oil off the archipelago's shores prompted the Argentina to file criminal charges against oil companies operating in the area.
Cristina Fernandez said an announcement by Premier Oil and Falklands Oil and Gas in April of a discovery of oil was a provocation. She also indicated that while the Islands, will be Argentine sooner or later, the South American nation isn't a threat to Britain or the Falklands and Argentina will continue to press for constructive dialogue to resolve the dispute.
London has argued that any dialogue with Argentina over the Falklands must have the consent from the Islanders and in that case it will include three sides: UK, Argentina and the Falkland Islanders.
Argentina rejects point blank such an option arguing that residents in the Falklands are an implanted population, 'don't exist as such' and in Cristina Fernandez words are 'squatters'.