Prime Minister David Cameron said he disagreed with Pope Francis I over the ownership of the Falkland Islands.
Pope Francis, who is the first Argentinian pontiff and a former Archbishop of Buenos Aires, has previously described the disputed islands as "Argentinian soil" which was "usurped" by Britain.
Mr Cameron has urged all world leaders, including the Pope, to respect the overwhelming 99.8% vote in this week's Falklands referendum in favour of remaining a British overseas territory.
In a reference to the method used by the Vatican to announce a decision on the identity of the new Pope, he said: "The white smoke over the Falklands was pretty clear."
Asked at a Press conference in Brussels whether he agreed with Francis on the issue of the Falklands, Mr Cameron said: "I don't agree with him – respectfully, obviously.
"There was a pretty extraordinarily clear referendum in the Falkland Islands and I think that is a message to everyone in the world that the people of these islands have chosen very clearly the future they want and that choice should be respected by everyone."
The Falklands War – known as the Malvinas by Argentina – began in April 1982 when Argentine forces invaded and occupied the Falkland Islands and South Georgia.
The British Government dispatched a naval task force to engage the Argentine Navy and Air Force, and retake the islands.