The decision, which is not yet final, follows a request by Argentina in 2009 to expand its maritime territory to include that of the islands, known as the Malvinas in Argentina.
The move would increase its waters in the South Atlantic Ocean by 35%.
The area is potentially rich in oil.
However, the UK government has played down the commission's ruling.
The Prime Minister's official spokeswoman said: "At this stage we have yet to receive details of [the] report. It is important to note that this is an advisory committee. It makes recommendations, they are not legally binding."
The Falkland Islands' government says the UN does not make changes in sovereignty in areas where the territory is disputed.
Mike Summers, chairman of the Legislative Assembly of the Falkland Islands, which governs the islands' internal affairs, 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."
The decision comes from the UN Commission on the Limits of the Continental Shelf.
Although not yet binding, the move raises the stakes in the claims by the UK and Argentina to the Falkland Islands region, whose waters are being closely explored for oil and gas deposits.
The Commission on the Limits of the Continental Shelf is a group of experts established under the 1982 United Nations Convention on the Law of the Sea, but it is not a United Nations' Commission.
The Commission notes that the islands are the subject of a dispute between the UK and Argentina, who went to war over the group in 1982.
Tuesday marks the anniversary of the ordering of the naval task force to the Falkland Islands by the then prime minister, Margaret Thatcher.
The UK has held the Falklands since 1833, and the vast majority of its 3,000 citizens want the islands to remain a British overseas territory.
Many islanders remain concerned about Argentina's claim as well as the potential for problems from rapid change brought by the oil exploration industry.
Drilling for oil in the territorial waters around the Falklands has been carried out despite opposition from Buenos Aires.
Shares in one of the companies drilling in the region, Rockhopper International, were down 9% on Tuesday.
The Falkland Islands have asked the UK to clarify the meaning of an international commission judgement that would leave the islands surrounded by Argentina's territorial waters.