It shows Argentine hockey captain Fernando Zylberberg running and exercising in the Falklands capital Port Stanley ahead of the London 2012.
The advert, which was broadcast in Argentina on Wednesday night, is titled Olympic Games 2012: Homage to the Fallen and the Veterans of the Malvinas.
It ends with the slogan: "To compete on English soil, we train on Argentine soil."
He told Sky News:
Member of Falkland Islands Legislative Assembly, Ian Hansen, said that the advert was filmed without permission.
He told the island's newspaper, the daily Penguin News:
Falklands War survivor Simon Weston has also condemned the advert
He told The Sun:
This is the latest measure by Argentina to reassert its claim to the British overseas territory it calls the Malvinas and follows months of political rhetoric between London and Buenos Aires on the issue.
Last month, was the 30th anniversary of the start of the Falklands War, when Argentine forces invaded the islands before being defeated by a British task force.