LIMA, Peru — As the possibility of an oil rush in their icy waters grows, the Falklands Islands are once again at the center of a diplomatic spat between the United Kingdom and Argentina.

Several British energy companies are now carrying out deep-sea exploration around the islands in the South Atlantic, known to Argentines as “las Malvinas” and which were the scene of a brief 1982 war that cost the lives of 904 soldiers from both countries.

One company in particular, Rockhopper Exploration, this week announced its discovery of what analysts believe may turn out to be a huge oilfield at its Sea Lion prospect, in an area known as the North Falklands Basin.

Rockhopper says it expects to shortly invest around $100 million in developing the field.

Meanwhile, two other companies have towed a huge drilling rig, the Leiv Eiricsson, from Greenland half-way around the world to make the most of the southern summer and continue their offshore search.

So it may be no coincidence that the long-running tension between Buenos Aires and London over the islands has once again flared up.

Read more: Argentines consider flaunting the Falklands at the Olympics

This week, British foreign secretary William Hague held talks with his counterparts from the South American trading bloc Mercosur, which includes Argentina, about access to their ports for vessels from the Falklands.

Hague described the talks as “productive and honest” and claimed that Chile, Brazil and Uruguay had all insisted they would not participate in any economic blockade of the Falklands.

He also claimed that the three countries would continue to allow ships from the islands to dock in their ports — provided they were sailing under other flags, in line with a decision adopted by Mercosur last month.

Argentina’s foreign ministry immediately responded, claiming that its neighbors were simply maintaining existing Mercosur policy by refusing to recognize the “illegal” Falklands flag. It also called on the UK to honor several UN resolutions that call for dialogue to resolve the islands’ sovereignty.

The fate of the Falklands is one of the last unresolved issues from the disintegration of Britain’s huge 19th Century empire. They have been under British control since 1833 although Argentina has always claimed that the islands — which lie 300 miles from its coast but thousands of miles from the British Isles — belong to it.

Most Britons had never heard of the remote, windswept archipelago until 1982 when the Argentine military dictatorship, desperate to shore up its popularity, invaded them, sparking a brief war which saw Britain retake the islands.

The British government now says that the islands’ tiny population, which overwhelmingly wants to remain part of the United Kingdom, has the right to self-determination under international law.

Argentina, however, focuses on the force used by Britain in the early 19th Century to occupy the archipelago and London’s refusal to hold wide-ranging talks about the dispute.