"To compete on English soil we train on Argentine soil," says the slogan at the end of the commercial, which aired late Wednesday.
The spot shows the captain of the Argentine national hockey team, Fernando Zyberberg, who is identified as an "Argentine Olympic athlete," training in the disputed islands with the Atlantic and penguins in the backdrop.
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Produced by the Argentine presidency, the commercial is called "Olympic Games 2012. Homage to the fallen and ex-combatants of the Malvinas."
Argentina and Britain fought a bloody 74-day war over the islands in 1982, known as the Malvinas in Spanish, and tensions between the two countries have flared anew 30 years later.
Falklands legislator Ian Hansen said he was disappointed that Argentina was airing a commercial that "seeks to politicize the Olympic Games in the service of its territorial ambitions."
"The video was filmed without the knowledge of the authorities on the islands," he said.
Zyberberg told FM Metro radio he spent a week running all over the island. "I've never trained as hard as during that week. I was in the mountains, on the road, the beach, the city, from 5:00 am," he said.
The Falklands war, which began with an invasion of the islands by Argentine forces, ended in their defeat and the deaths of 649 Argentine soldiers and 255 British troops.
