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:
– The Foreign Secretary, William Hague
"Argentina has had some diplomatic setbacks in the last few weeks. They have failed at summit of the Americas to get other countries - South and North America - to issue a declaration on the Falkland Islands.
"I think what is happening is they are looking for one or two stunts to try and make up for that or save a bit of pride somehow.
But I don't think trying to misuse the Olympics in some way for political purposes will go down very well with other countries.
"Of course, it doesn't change our position on the Falkland Islands. We will always support the right to self-determination of the people of the Falkland Islands."
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:
– Member of Falkland Islands Legislative Assembly, Ian Hansen
"We determine our own future, and we will not be bullied by the Argentine government, neither by their attempts to undermine our economy, nor by their constant misrepresentation of the truth, nor by pieces of cheap and disrespectful propaganda such as this"
Falklands War survivor Simon Weston has also condemned the advert
He told The Sun:
– Simon Weston, Falklands veteran
"It will achieve nothing other than fuelling an argument. The hockey player doing step-ups on the war memorial is an absolute insult. I hope the Olympic authorities will see this for what it is and take action."
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.