Several hundred demonstrators pelted police officers with homemade firebombs and threw rocks and flaming bottles at the embassy as a series of events were held in Argentina and the UK on Monday to commemorate the 1982 conflict.
Television footage showed riot police using a water cannon to disperse the group of extremists, who had earlier set fire to a union flag and an effigy of the Duke of Cambridge in protest against British rule of the islands.
The violence came after the Argentinian president, Cristina Fernández de Kirchner, stoked the diplomatic battle between Buenos Aires and London by describing the UK's control over the Falklands as unjust.
However, David Cameron said he remained committed to upholding British sovereignty over the territory and insisted the islanders must be allowed to choose their nationality.
Argentina's complaints – including to the United Nations – of "militarisation" by the UK will be heightened by the deployment on Wednesday of the Royal Navy's most advanced warship for its maiden operation.
Destroyer HMS Dauntless will set sail from Portsmouth for the Falklands in what the the Ministry of Defence says is a "pre-planned and routine" six-month deployment in the South Atlantic.
It comes after Argentinian hackles were raised by the "provocative" six-week deployment of Prince William to the islands as an RAF search and rescue helicopter pilot.
The Foreign Office condemned "the violent actions of a minority" following the demonstration.
It said: "All states are obliged under the Vienna convention to provide appropriate protection for foreign diplomatic missions.
"We expect the Argentine government to continue to fulfil its obligations under the convention and continue fully to enforce the law against any demonstrators committing criminal acts."
Britain saw 255 of its servicemen killed in retaking the remote South Atlantic islands in 1982, while 649 Argentinians lost their lives in the conflict.
In the UK, war widows attended a service of remembrance at the National Memorial Arboretum's Millennium chapel to mark the anniversary. A single candle was lit and will be left alight for the 74 days of the conflict.
In Argentina, however, Fernández used the commemorations to make a renewed push to wrest back control of the islands, describing Britain's stance as "ridiculous and absurd".
She called for talks on ending the "unjust" situation – something London has ruled out for as long as no change is demanded by the islanders themselves.
Cameron – who like Fernández included the enemy dead in his anniversary message – insisted Britain was no less committed now than in 1982 to protecting the right to self-determination.
"Britain remains staunchly committed to upholding the right of the Falkland Islanders, and of the Falkland Islanders alone, to determine their own future," he said.
"That was the fundamental principle that was at stake 30 years ago, and that is the principle which we solemnly reaffirm today."
It was, he said, "a day to remember all those who lost their lives" on both sides as well as to "salute the heroism of the task force" sent to correct a "profound wrong".
His words were echoed by the defence secretary, Philip Hammond, who also dismissed warnings from former military chiefs that the UK would be unable to defend the islands from a new invasion.
"We will defend them robustly. We have the assets, the people, the equipment in place to do so," he said in response to comments by the man who led the task force, Admiral Sir John Woodward.
The lack of an aircraft carrier would make a repeat impossible, the ex-navy chief told the Times.
Hammond noted, however, there was "not the slightest intelligence to suggest that there is any credible military threat to the Falklands".
Spurred on by the discovery of oil reserves off the Falklands, Fernández has spearheaded an intense reassertion of Argentina's claim over what it calls las Malvinas.
It has secured the support of other South American countries for a ban on Falkland-flagged ships in their ports and is seeking to restrict flights as part of an economic squeeze.
At the weekend, Argentina threatened legal action against British and American banks involved in advising UK companies exploring for oil.
The foreign secretary, William Hague, who has led a push to improve UK trade and other links with South America, described Argentina's recent aggressive actions as "deeply regrettable".
