Rockhopper, a London-listed oil exploration firm, is battling to slow an investor sell-off after Argentina's president vowed to sanction any oil companies operating near the Falkland Islands.

In a national address, Javier Milei emphasised Argentina's claim over the British territory and promised to sanction any oil companies working there as part of what he called the "British occupation".

Shares in Rockhopper, which is working with partner Navitas on the Sea Lion oil field north of the Falklands, fell more than 10 per cent to 69p in early trading.

Sea Lion, discovered in 2010, is the Falklands basin's largest find and the territory's first oil development, but it has spent more than a decade trying to secure the funding needed to move to production. Argentina has long objected to hydrocarbon exploration around the islands, and Argentine governments have previously sought to discourage international involvement through legal and diplomatic pressure, though companies have continued to drill under licences issued by the Falkland Islands Government.

Milei singled out the Sea Lion oil project, describing it as a "clear and present danger" to Argentina's claim to the islands.

"If we do not act swiftly in a few months, they will have the material capacity to access the oil that lies underneath our sea. Something that has never happened before," he said.

Rockhopper and Navitas rushed to soothe investor fears, insisting that they do not expect Argentina's threats to have a "material effect" on their delivery of oil from the area.

The oil firms said: "The partnership operates pursuant to valid petroleum licenses lawfully granted to it by the Government of the Falkland Islands, a self-governing UK Overseas Territory, and with the full and ongoing support of the UK Government.

"The partnership believes that the recent developments are not expected to have a material effect on the development activities of the Sea Lion Project, including the timetable for completion of the Project's development."

Rockhopper, which is based in Salisbury, has said it expects to start delivering oil from the Sea Lion project at the start of 2028. It has contributed $350m (£259m) in debt to the project and owns 35 per cent of the venture.

Miliband: UK claim to Falklands 'unwavering'

Milei's hotly-anticipated address has ramped up tensions between Argentina and the UK, whose control over the territory was last threatened during the 1982 Falklands War.

Controversy over the islands returned to relevance earlier this summer, when a number of Argentinian footballers were condemned for holding up a banner supporting their country's claim to the Falklands after their semi-final victory against England at the World Cup.

"The Falklands are Argentinian. Historically and legally. There can be no argument. They are part of the Argentine territory," the President said.

"The islanders on their usurped territory do not have a legitimate right to self-determination and any argument on any such self-determination is invalid."

The UK government was quick to condemn Milei's comments. Foreign Secretary Ed Miliband said the UK's ownership of the Falklands is "unwavering".

He wrote on X: "The Islands are British and will remain so because that is the overwhelming position of the Islanders.

"Their right of self-determination is paramount, grounded in international law and we will resolutely uphold it."

Defence Secretary Wes Streeting said Britain's commitment to the territory is "absolute and unshakeable". Milei's statement "tells us more about domestic politics in Argentina than it does about the Falklands Islands," he said.

John Binns, a partner at BCL solicitors and a sanctions specialist, said the legitimacy of Milei's threat against Rockhopper is "in the eye of the beholder".

"The truth is that the power of sanctions, especially when they are unilateral, depends not on the merits of the cause but on the power of the state imposing them. The UK may well respond to Argentine sanctions with something of a shrug, at least for now," he said.