Representatives of the Falkland Islands went to the United Nations in New York on Thursday to defend their right to remain a British territory, as Argentina renewed its claim on the archipelago which it knows as the Malvinas.

The Argentinian foreign minister, Héctor Timerman, was addressing the UN's special committee on decolonisation to restate Argentina's calls for the UK to enter negotiations over the sovereignty of the south Atlantic islands.

But Falklands legislative assembly members Sharon Halford and Mike Summers were also appearing before the committee to rebuff Timerman's demands, and to urge the UN to respect the overwhelming result of this year's referendum, in which islanders voted by 1,513 to three to remain a British overseas territory.

The committee has previously backed Argentinian calls for negotiations over sovereignty, but the Foreign Office in London insisted that body "no longer has a relevant role to play" with respect to British overseas territories, arguing that it was insulting to describe their relationship with the UK as colonial.

Halford said that the message from the referendum in March was clear: "We, the people of the Falklands, are happy with our current relationship with the UK. It is not an anachronistic or colonial situation as characterised by Argentina, but a modern relationship where the UK listens to our wishes and we are responsible for our own internal self-government."

She told the committee: "I hope that the islanders have spoken loudly enough for people to hear them around the world."

Summers said that the committee had previously "prioritised the interests of certain member states over the wishes of the peoples it is supposed to be assisting" and urged members to "examine their collective conscience" and support Falklanders' right, under successive UN resolutions, to self-determination.