In England, a memorial service was held at the national war memorial to remember the 255 British troops, 649 Argentineans and three islanders who died in the 1982 conflict.
A candle was lit and will be left burning for 74 days to mark the period the conflict lasted.
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The remembrance service came amid heightened tensions between Britain and Argentina, which has recently been reasserting its claim to the islands.
In Argentina, President Cristina Fernandez announced she's asked the International Red Cross to persuade Britain to let its experts identify unknown soldiers buried in the Falkland Islands.
Her much-anticipated speech on the anniversary of Argentina's April 2, 1982 invasion of the islands they claim as the Malvinas was focused on promoting dialogue and understanding.
She said her government sets a global standard for protecting human rights and vowed to "respect the interests of the islanders" if Argentina manages to peacefully regain control over the archipelago.
"We don't have war drums, nor do we wear military helmets. Our only helmets are those of construction workers, working for the inclusion of all," she said in a brief speech at the Monument to the Fallen.
In London, Prime Minister David Cameron said Britain had to come to the islanders' defence in 1982, and will do so again if anyone tries to deprive them of their liberty.
The 74-day occupation ended when British troops routed the ill-prepared Argentines in hard-fought trench warfare.
Fernandez called Cameron's statement absurd and ridiculous, noting that Argentines were also deprived of their liberty at the time, living under a 1976-1983 dictatorship, supported by outside powers, that had kidnapped and killed thousands of its own people.
"I am proud of having made promoting human rights one of the pillars of our state," she said, adding that for this reason it's impossible to consider that Argentina would not also protect the rights of the 3000 islanders.
Britain has refused Argentina's repeated calls to negotiate the islands' sovereignty, saying it's up to the islanders to decide.
Britain has controlled the Falklands since 1833 and the islanders overwhelmingly say they want to remain British.
The Royal Navy said one of its newest warships, the HMS Dauntless, will set sail for a six-month deployment to the South Atlantic on Wednesday. The Ministry of Defence said it was a routine mission.
