Britain and Argentina fought a 10-week war in 1982 over the South Atlantic islands, which are part of Britain's self-governing overseas territories.
Cristina Fernandez de Kirchner, the Argentine president, has marked the 30th anniversary of the conflict with a sustained diplomatic campaign to assert Argentina's sovereignty claim.
The Falklands cause is a popular rallying cry in Argentina but the stakes have also been raised by oil exploration in the waters around the islands.
In her letter, Ms Fernandez accused Britain of breaching UN resolutions urging the two countries to negotiate a solution to the dispute over the Falklands, known in Argentina as Las Malvinas.
"The question of the Malvinas Islands is also a cause embraced by Latin America and by a vast majority of peoples and governments around the world that reject colonialism," she wrote.
Britain's Foreign Office rejected the call for negotiations, sticking to London's long-established stance that the approximately 3,000 people of the Falkland Islands had chosen to be British.
"There are three parties to this debate, not just two as Argentina likes to pretend. The islanders can't just be written out of history," the Foreign Office said.
"As such, there can be no negotiations on the sovereignty of the Falkland Islands unless and until such time as the islanders so wish."
The islanders are to vote this year in a referendum on whether they want to stay part of Britain's self-governing overseas territories. They are expected to vote overwhelmingly in favour of the status quo.