Last week, Sean Penn, the Hollywood actor, appeared with President Cristina Fernandez de Kirchner to criticise British actions over the disputed archipelago.
But a group of Argentina's leading intellectuals, historians, journalists, constitutional experts and politicians have published an open letter calling on their own government to rethink policy towards the islands they call the Malvinas branding it "crazy" and "absurd".
The 17 signatories accused Mrs Kirchner's government of "harassing" the Falklands population of 3,000, who overwhelmingly want the islands to remain a British Overseas Territory.
The group said Argentina must respect the islanders' right to self-determination and give up its policy of trying to force Britain into negotiating sovereignty.
"It is truly absurd and crazy to force a government and sovereignty on people who do not want it," commented Fernando Iglesias, a former congressman who co-authored the document.
This year marks the 30th anniversary of the Falklands conflict and concerns have risen over the increasingly hostile rhetoric emerging from Argentine politicians who claimed Britain was treating the islands as "the last refuge of a declining empire".
The Argentine government accused Britain of an "act of provocation and aggression" by sending The Duke of Cambridge to the islands on a six-week tour of duty as an RAF search and rescue pilot.
It also accused Britain of "militarising" the South Atlantic with its decision to send the state-of-the art naval war ship HMS Dauntless to the area and early this month said it would appeal to the United Nations to negotiate the issue of sovereignty.
Last week the visit to the Falkland Islands by David Willetts, the universities minister, who stopped off en route to the Antarctic, served to inflame tempers.
And news that a delegation of MPs is expected to travel to the remote islands later this year to evaluate defences led to accusations that Britain was escalating the dispute.
Argentina stepped up its claims to the Falklands when British companies began drilling for oil in the South Atlantic in early 2010. It has since ceased direct flights to the islands and lobbied neighbouring countries to do the same.
Another of the signatories, historian Luis Alberto Roberto, argued that President Kirchner's policies towards the islands were proving counterproductive, and that the government should be looking to forge links with the islanders not isolate them.
"In 1982 we resorted to force. We destroyed what had been achieved over many years. We created perfectly justified hate and fear. We lost the Malvinas. And, furthermore, we lost many Argentinians."
Argentina seized the Falklands by force in April 1982 but the islands were retaken by British troops in a 74 day war that cost the lives of 258 British servicemen and 649 from Argentina.
Philip Hammond, the Defence Secretary, insisted this week that there was "no current credible military threat" from Argentina but added: "Her Majesty's Government is committed to defending the right of the Falkland islanders to self determination and plans exist for rapid reinforcement of the land, sea and air forces in and around the islands, should any such threat appear."