However, Downing Street said the commission had yet to publish its report and that its findings had no legal force.
The Prime Minister’s spokeswoman said: “At this stage we have yet to receive details of that report. It is important to note that this is an advisory committee. It makes recommendations, they are not legally binding.
“Speculation about what the report says has come from Argentina. I think we should wait to see what comes from the commission in New York.”
Earlier, the Argentine foreign ministry said the commission had ruled that its territorial waters in the South Atlantic should be expanded by 35 per cent – an increase of 0.66 million square miles.
“This is a historic occasion for Argentina because we’ve made a huge leap in the demarcation of the exterior limit of our continental shelf,” said foreign minister Susana Malcorra.
“This reaffirms our sovereignty rights over the resources of our continental shelf.”
The report heightened concerns among the islanders that Argentina’s claim could threaten their expanding oil exploration industry which has already pumped millions of pounds into their economy.
However Downing Street made clear that the UK would continue to back their right to self-determination in the face of the claims from Buenos Aires.
“What is important is what the Falkland Islanders themselves think,” the Prime Minister’s spokeswoman said.
“We will continue to support their right to determine their own future.”
The Falkland Islands government said it was seeking clarification from London as to the implications for the islands of any ruling by the commission.
Mike Summers, the chairman of the islands’ Legislative Assembly, said: “Our understanding has always been that the UN would not make any determination on applications for continental shelf extension in areas where there are competing claims.”