Two UN resolutions and one constitutional clause: the ground Argentina rests its Malvinas claim on
Background
Argentina's Foreign Ministry has set out in an official statement the legal ground of its claim over the islands. It says the international community has recognised for decades a sovereignty dispute over the Islas Malvinas, South Georgia and the South Sandwich Islands and the surrounding maritime spaces. It cites United Nations General Assembly Resolution 2065 (XX), which invited the governments of Argentina and the United Kingdom to resume negotiations without delay for a peaceful solution, and Resolution 31/49, which urged both parties to refrain from unilateral changes while the process remained open — Argentina argues that unilateral exploitation of non-renewable resources in the disputed area is such a change. Both states are parties to the United Nations Convention on the Law of the Sea and accepted the compulsory procedures leading to binding decisions set out in its Part XV. The statement rests Argentina's commitment to respecting the islanders' way of life on the First Transitory Provision of the National Constitution, and rejects the application of the principle of self-determination to the present inhabitants.
In plain words
Resolution 2065 (XX) — The 1965 UN General Assembly resolution inviting Argentina and the United Kingdom to negotiate over the islands.
First Transitory Provision — The clause of Argentina's Constitution that states its sovereignty claim over the islands and its respect for the islanders' way of life.