Nearly three decades on from the Falklands War, the obscure archipelago known in South America as Las Malvinas is a source of rising political tension once again. But simply ignoring Buenos Aires' claims of sovereignty will not make them go away.

The latest development is the decision by Mercosur – a trading bloc comprised of Argentina, Brazil, Paraguay and Uruguay – to close its ports to ships flying under the Falkland Islands flag. The tangible impact may not be huge, given that there are only about 25 such boats, most of them fishing vessels. But the ban is part of an escalating campaign by the Argentine President Cristina Kirchner that, unlike the 1982 invasion, is drawing increasing support from across the region. As Ms Kirchner's Uruguayan counterpart said of the Mercosur decision: "We hold nothing against the UK. But we have a lot in favour of Argentina."

In part, Buenos Aires has an eye on the four billion barrels of oil estimated to be locked under the sea around the Falklands. The issue of sovereignty resurfaced when Britain started drilling in the region in 2010, a move that sent Argentina to the United Nations asking for help stopping any more "unilateral acts" and pressing for talks over the disputed territory. A series of oil strikes since have only upped the pressure. And although it is not yet clear whether the predictions of vast reservoirs of hydrocarbons will be borne out, Ms Kirchner's attempts to couch the issue in terms of defending regional resources is striking a chord with her neighbours.

So far, the British Government has refused all requests to reopen negotiations and stresses the right of islanders to decide their own political future. Such rights are certainly to be protected. But it is also the islanders who are bearing the brunt of the diplomatic wrangling. New laws requiring ships passing through Argentinian waters to carry permits are taking their toll on the local fishing industry, and there have been threats that the only air link off the islands could be suspended. It is time to defuse the situation. Last year, Hillary Clinton suggested she broker talks between Britain and Argentina. We should take her up on the offer.