Representatives of the islands' government are flying to London to join Foreign Secretary William Hague for talks with Argentine foreign minister Hector Timerman.
The Legislative Assembly of the Falkland Islands stressed that the representatives, Dick Sawle and Jan Cheek, would not be "negotiating any deal".
"We are anticipating a full and frank exchange of views," the assembly said. "We look forward to giving Mr Timerman some direct messages on the unacceptability of Argentina's actions against the Falkland Islands. We demand that our rights be respected, and that we be left in peace to choose our own future."
Argentine President Cristina Fernandez de Kirchner has strongly asserted her country's demands for the Falklands to come under its sovereignty despite the opposition of the islanders.
This month, she had an advert published in British newspapers claiming that Argentina had been stripped of the islands in "a blatant exercise of 19th century colonialism".
David Cameron insists the residents of the Falklands must decide their own future, and a referendum on the islands' political status is to be held in March.