Port Stanley, Falkland Islands (CNN) -- Britain on Wednesday dismissed a complaint from Argentina about the "militarization of the South Atlantic" as tensions rise regarding the Falkland Islands, over which the two countries fought a war 30 years ago.
"The people of the Falkland Islands are British out of choice," the British Foreign Office said in a statement. "They are free to determine their own future, and there will be no negotiations with Argentina on sovereignty unless the Islanders wish it."
It was responding to a warning from Argentinian President Cristina Fernandez de Kirchner that her country would file a protest at the United Nations.
"I have instructed our chancellor to formally present before the U.N. Security Council and the U.N. General Assembly this militarization of the South Atlantic, which implies a great risk for international safety," she said during a speech in Buenos Aires.
"We're going to file a protest," Fernandez said.
Royal visit, oil fuel Falklands tension
Kirchner to UK: 'Give peace a chance'
Colourful houses made from corrugated iron give the Stanley, the capital of the islands, a Scandinavian feel.
British Royal Navy frigate HMS Antelope explodes in the bay of San Carlos off East Falkland during the 1982 Falklands conflict.
Britain and Argentina's sovereignty standoff
No protest had been filed as of Wednesday afternoon, U.N. spokesman Martin Nesirky.
Speculation in recent days had been that she would cut the Falklands air link to the South American mainland by banning the airline LAN Chile from using Argentinian airspace to fly to the islands from Chile. The Saturday flights are the only scheduled air service to the Falklands and carry fresh food as well as passengers.
The president made no such announcement in her speech Tuesday.
Why tensions are flaring over Falklands
Argentina already bans Falklands ships from its ports, an action joined by other South American and Caribbean nations.
"I guess we were all kind of relieved that there wasn't anything particularly concrete. It seems to be another burst of hot air really -- and to that degree -- we're relieved," said John Fowler, a journalist and Falkland Islands resident.
Britain and Argentina fought a war over the Falkland Islands, which Argentina calls Las Malvinas, in 1982. Though Britain won the war, expelling an Argentinian military force, Argentina claims the territory, which has been under British rule since 1833, as its own. Britain maintains that the 2,500 residents of the Falklands have the right to determine their allegiance, and so far that has been staunchly British.
"The UK has no doubt about our sovereignty over the Falklands. The principle of self-determination, as set out in the U.N. Charter, underlies our position," the Foreign Office said.
British Prime Minister David Cameron said residents have a right to decide.
"We support the Falklands' right to self-determination, and what the Argentinians have been saying recently I would argue is actually far more like colonialism, because these people want to remain British, and the Argentinians want them to do something else."
Addressing Cameron directly in her speech, Fernandez said: "I simply want to ask the prime minister of England to give peace a chance."
Tensions between London and Buenos Aires were raised even higher this month when Britain sent Prince William to the Falklands as a military helicopter pilot.
The prince's deployment comes as Britain is making other moves to support its 1,700 personnel at the Mount Pleasant military complex in the Falklands.
"We are having what in game theory is called tit-for-tat ... I don't see an end in sight right now, but I'm sure that war is not the end," Federico Merke, a professor of international relations at San Andres University, said after the president's speech.
So why, besides supporting the Falklands' inhabitants, does Britain want to hang on to the islands? The answer may lie in the lucrative fishing grounds around the islands as well as a growing oil drilling industry.
Argentina, of course, has economic interests as well, but analysts say the current standoff has much to do with internal politics.
"The government is being squeezed from lots of different areas, so one way to distract from the economic problems facing the country is to raise the Malvinas issue," said Mark Jones, an expert in Latin American politics at Rice University in Texas. "It's one of the few issues outside football that you can get universal consensus on."
CNN's David Wilkinson, Dan Rivers, Brad Lendon and Richard Roth contributed to this report.
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A Falklands Five pound note issued by the Falkland Islands Government; the disputed islands, which Argentina calls Las Malvinas, are viewed by Britain as a British Overseas Territory, like Bermuda or Gibraltar.
Outside Stanley, the Sapper's Hill minefield is being slowly cleared of mines by a private contractor BACTEC. 113 minefields have been identified containing some 13,000 mines.
Several species of penguins inhabit the Falkland islands.
British troops arriving in the Falklands Islands during the 1982 Falklands conflict
A line of British soldiers in camouflage advancing during the 1982 Falklands conflict.
Britain's Prince William is is being deployed to the Falkland Islands on a six-week tour of duty as a search and rescue helicopter pilot.
David Cameron has accused Argentina of "colonial" attitudes towards the Falklands.
Argentinian President Cristina Fernandez de Kirchner has asserted her country's sovereignty of Las Malvinas.
A man stands next to a map of the Falkland Islands reading 'They are Argentinian' during a demonstration in front of the British embassy in Buenos Aires in January.
Argentinian activists burn a Union Jack during a demonstration in front of the British embassy in Buenos Aires in January.
Argentinian war veterans and relatives march with torches in Buenos Aires during the 28th anniversary of the 1982 conflict.
British Prime Minister Margaret Thatcher meets personnel aboard the HMS Antrim during a visit to the Falkands in 1983.
British Prime Minister Margaret Thatcher and her husband Denis, left, visit Stanley Junior School, Stanley on the Falkland Islands in 1983.
Pictured in 1980, leaders of Argentina (left to right): President General Jorge Rafael Videl, Admiral Armando Lambruschini , General Leopoldo Galtieri and Brig Gen O Domingo Graffigna.
Sukey Cameron hands in a petition at Downing Street demanding full British citizenship to 300 Falkland islanders whose grandparents were not born in Britain, 25th September 1981.
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