Argentina's president has described the UK's control over the Falkland Islands as unjust, as services are held in both Britain and Argentina to mark the 30th anniversary of the start of the war.
Cristina Fernandez described the UK's stance as "absurd", but urged peace.
UK PM David Cameron said the day should remember the dead from both countries.
A total of 255 British servicemen and about 650 Argentines died after the UK sent a task force following the Argentine invasion on 2 April 1982.
In a statement, Mr Cameron also said that he remained committed to upholding British sovereignty over the islands.
Meanwhile, the Royal Navy has confirmed one of its newest warships, HMS Dauntless, will leave the UK on Wednesday for a six-month routine deployment in the South Atlantic.
Britain has controlled the Falklands since 1833 but Argentina claims the territory - which it calls the Malvinas - saying it inherited rights to them from Spain.
Day for reflection
British veterans of the war - and relatives of those who died - paid their respects at Britain's National Memorial Arboretum in Staffordshire.
A single candle was lit as a gesture to mark the anniversary. It will remain alight for 74 days - the length of the conflict.
Anglican priest the Rev Vic Van Den Bergh told the service they had come together to pray for peace between the UK and Argentina and to remember the fallen - including the three Falkland Islanders who died in the conflict.
In his statement, Mr Cameron said: "Thirty years ago today the people of the Falkland Islands suffered an act of aggression that sought to rob them of their freedom and their way of life.
"Today is a day for commemoration and reflection: a day to remember all those who lost their lives in the conflict - the members of our armed forces, as well as the Argentinian personnel who died."
Mr Cameron saluted the "heroism" of the soldiers, sailors, airmen and marines who took part in the operation which freed the islanders from Argentine rule and said the UK played a role in "righting a profound wrong".
He said: "Britain remains staunchly committed to upholding the right of the Falkland Islanders, and of the Falkland Islanders alone, to determine their own future.
"That was the fundamental principle that was at stake 30 years ago: and that is the principle which we solemnly reaffirm today."
Argentina's President Cristina Fernandez de Kirchner gave a speech at the southern port of Ushuaia, where crowds gathered to remember the Argentine servicemen who died.
The president paid tribute to the "hundreds who came to fight here, to this territory, to the islands, and to the hundreds who laid down their lives".
She attacked the UK government's stance on the Falkland Islands, saying: "Every day that goes by it looks more ridiculous, more absurd to the eyes of the world."
President Kirchner went on: "It is an injustice that in the 21st Century there are still colonial enclaves... 16 colonial enclaves throughout the world - 10 of those belonging to the United Kingdom."
She added: "We also demand that so they stop usurping our environment, our natural resources, our oil."
But she said that "wars only bring backwardness and hatred" and said the government supported peace.
The president said she had written to the International Red Cross to urge the UK to "take necessary measures" to identify unknown soldiers from both countries who are buried in the Falkland Islands.
Before she arrived in Ushuaia, about 5,000 people, including Argentine veterans, held a vigil for the fallen.
Army veteran Carlos Alberto Latorre said he saw himself as one of the "Malvinas combatants" and it was important for him to be there to educate Argentines about what happened during the conflict, Reuters reported.
He said he could see younger generations also believed Argentina had a rightful claim to the islands, and this gave him the strength to continue.
Meanwhile, members of left-wing political group Quebracho burning a union jack and an effigy of Prince William, who was deployed to the territory in March, during a demonstration near the British embassy in Buenos Aires.
British Falklands War veteran Simon Weston, who was badly injured when his ship Sir Galahad was attacked, told the BBC he did not believe that Argentina's military capability was as strong a threat as it was at the time of the initial conflict.
Richard Jones, whose son Craig was the last soldier to be killed in the conflict, said those who lived on the islands identified themselves as British.
"They're not Latin American, they've got nothing really in common with the Argentines. They are as British stock as we or anybody else. They want to remain - they don't want to be part of Argentina, and that was what the war was all about," he said.
Argentina has asked for negotiations about sovereignty, but the British government says it will not discuss the issue without the agreement of the islanders.
Foreign Office Minister Jeremy Browne said although the relationship with Argentina "was somewhat fraught", the UK was not entirely friendless in Latin America, while Defence Secretary Phillip Hammond said the UK had "the assets, people and equipment" in place to robustly defend the Falkland Islands.
In a statement, shadow defence secretary Jim Murphy said there was no evidence the Falkland Islanders wished to change their nationality and added: "Something more important than the Empire's legacy was and is at stake: the universal right to self-determination and our belief that diplomatic dispute should be resolved by democracy rather than the uptake of arms."
London has accused Buenos Aires of trying to impose an economic blockade on the islanders, after it banned Falklands-flagged ships from docking in its ports, as well as those of other countries which are members of the Mercosur trading block.
On Monday Downing Street also dismissed Argentina's threat to take legal action against companies involved in oil exploration in the islands.
The prime minister's official spokesman said: "We are a big investor in that country. We think they are acting against their interests if people are attacking shops and branches of banks in Argentina."
Argentina has complained about what it calls British "militarisation" in the south Atlantic.
BBC world affairs editor John Simpson said while a new armed conflict remained unlikely, Argentina was now using diplomatic weapons to push its claim over the Falklands.
The defeat of the Argentine forces led directly to the collapse of the military dictatorship led by Gen Leopoldo Galtieri, who was later jailed in Buenos Aires for "incompetence" during the war.
The British prime minister at the time was Margaret Thatcher, but she is not expected to play a part in the commemoration of the 30th anniversary because of ill-health.