Argentine President Cristina Fernandez sent a letter to Prime Minister David Cameron that demanded the United Kingdom enter into negotiations over the sovereignty of the islands, which Fernandez said were forcibly stripped from Argentina 180 years ago.
Fernandez said Cameron should give the islands back.
A spokesman for Cameron said the people of the Falklands have shown a "clear desire to remain British" and that Cameron would "do everything to protect the interests of the Falkands islanders."
The Guardian newspaper said the islanders will vote in a referendum in March, and the results are expected to overwhelmingly support the territory remaining British.
The British Foreign and Commonwealth Office has ruled out any negotiations and said islanders must decide the future of the Falklands.