A sign on a minefield between Port Stanley and Goose Green, Falklands, 11 March 2013. (Photo: EPA / JAVIER LIZON) 
The request to resume talks is the latest chapter in Argentina's long-held claim over the British-run islands, which included the 1982 war. The islands are located in the South Atlantic about 600 kilometres from the Argentinian mainland.
Argentina's Foreign Minister, Santiago Cafiero, "formulated a proposal to restart negotiations for sovereignty over the Falklands Question" in a meeting with his British counterpart James Cleverly during a summit in India, the Foreign Ministry said.
The Argentinian government also invited the UK to "hold a meeting to settle" the debate at the United Nations.
British foreign minister Cleverly responded in a tweet: "The Falkland Islands are British. Islanders have the right to decide their own future - they have chosen to remain a self-governing UK Overseas Territory."
A 2013 referendum on the islands, known as Las Islas Malvinas in Spanish, resulted in a 99.8% vote to remain British.
(Reporting by Maximilian Heath in Buenos Aires; Additional Reporting by Alistair Smout in London; Writing by Isabel Woodford; Editing by Matthew Lewis.)