The future of the Falkland Islands is in the hands of the people who live there, not Argentina, the prime minister has insisted.
David Cameron rebuffed claims by Argentine president Cristina Fernandez de Kirchner that Britain is a colonial power and that the Islands should be handed over.
Cameron told her she should "listen" to the result of a referendum to be held on the Island, and if the people chose to remain British they would have his "100%" backing.
Cristina Fernandez de Kirchner reignited the row over the future of the Falkland Islands
"The future of the Falkland Islands should be determined by the Falkland Islanders themselves, the people who live there," he said.
"Whenever they have been asked their opinion, they say they want to maintain their current status with the United Kingdom.
"They're holding a referendum this year and I hope the president of Argentina will listen to that referendum and recognise it is for the Falkland Islanders to choose their future, and as long as they choose to stay with the United Kingdom they have my 100% backing."
Cameron, on a visit to Preston, responded to questions on the Islands after the row over their future was reignited by an open letter written by the president of Argentina, calling on him to relinquish British control.
Cameron rebuffed claims by Argentine president Cristina Fernandez de Kirchner that Britain is a colonial power
The letter, published as an advert in the Guardian and reported in other newspapers, said that Argentina was forcibly stripped of the Malvinas - the Argentinian name for the islands - in "a blatant exercise of 19th century colonialism".
The 59-year-old president, who made several calls for the return of the islands during last year's 30th anniversary of the two countries going to war, urged the prime minister to abide by United Nations resolutions whicih she says back the Argentinian cause.
"One hundred and eighty years ago on the same date, January 3rd, in a blatant exercise of 19th century colonialism, Argentina was forcibly stripped of the Malvinas Islands, which are situated 14,000km (8,700 miles) away from London," she said in the letter, copied to United Nations secretary general Ban Ki-moon.
"The Argentines on the Islands were expelled by the Royal Navy and the United Kingdom subsequently began a population implantation process similar to that applied to other territories under colonial rule.
"Since then, Britain, the colonial power, has refused to return the territories to the Argentine Republic, thus preventing it from restoring its territorial integrity.
"The question of the Malvinas Islands is also a cause embraced by Latin America and by a vast majority of peoples and governments around the world that reject colonialism."
Cameron and de Kirchner clashed over the Falklands when the pair came face to face at the G20 summit in Mexico last June.
He rejected her demand for negotiations over the sovereignty of the islands and told her to respect the result of a referendum, when the Falklanders will vote on whether they wish to retain their ties with Britain.
In December Argentina protested at Britain's decision to name a vast swathe of Antarctica Queen Elizabeth Land, with its foreign ministry handing a formal protest note to British ambassador John Freeman in Buenos Aires.
The area, which makes up around a third of the British Antarctic Territory, is also claimed by the South American country.
De Kirchner's letter continues: "In 1960, the United Nations proclaimed the necessity of 'bringing to an end colonialism in all its forms and manifestations'.
"In 1965, the General Assembly adopted, with no votes against (not even by the United Kingdom), a resolution considering the Malvinas Islands a colonial case and inviting the two countries to negotiate a solution to the sovereignty dispute between them.
"This was followed by many other resolutions to that effect.
"In the name of the Argentine people, I reiterate our invitation for us to abide by the resolutions of the United Nations."
Barry Elsby, a member of the Islands' Legislative Assembly, said: "We understand that the Argentine government has put out a letter that both calls our home a colony and claims that the United Kingdom is ignoring United Nations General Assembly resolutions.
"We are not a colony; our relationship with the United Kingdom is by choice.
"Unlike the government of Argentina, the United Kingdom respects the right of our people to determine our own affairs, a right that is enshrined in the UN Charter and which is ignored by Argentina."
A Foreign Office spokeswoman said the Falkland Islanders "are British and have chosen to be so".
"They remain free to choose their own futures, both politically and economically, and have a right to self-determination as enshrined in the UN Charter," she added.
"This is a fundamental human right for all peoples. There are three parties to this debate, not just two as Argentina likes to pretend."