"To compete on English soil, we train on Argentine soil," is the slogan closing the advert aired on Wednesday night with Fernando Zylberberg of the Argentine men's hockey team on a training run past several landmarks on the British-held islands.
Controversy is already raging about the advert, with The Sun's front page on Friday accusing Argentina of "dancing on our graves", referring to Zulberberg using the steps of a British war memorial in his training.
Ian Hansen of the Falkland Islands Legislative Assembly called it "cheap propaganda", while Falklands veteran Simon Weston said the film - which was made without permission from island authorities - was "as low as it gets".
Argentines were also reportedly critical, with Buenos Aires newspaper La Nacion saying many see it as a stunt to make political capital by president Cristina Kirchner's government.
The advert contradicted the government's recent denial that the south American country would seek political gain from the London Games which take place from July 27 to August 12.
Argentina claims sovereignty over the islands in the south Atlantic which Argentines call Las Malvinas.
President Cristina Fernandez de Kirchner's government has pushed hard for negotiations with Britain this year, the 30th anniversary of Argentina's 1982 invasion that sparked a short war won by Britain with the loss of more than 900 lives on both sides.
The advert was aired on the 30th anniversary of the sinking of Argentine ship the General Belgrano during the war.
Zylberberg, who was on the islands last month with many Argentine participants in the Falklands marathon, was filmed doing exercises outside the Globe Tavern in the islands' capital Port Stanley and running past the offices of the Penguin News newspaper.
"The idea was to get the message through that the Malvinas are Argentine," Zylberberg told the Cadena 3 radio station in an interview about the clandestinely filmed advert.
"I spent a whole week running on the island. It was an incredible experience because we were surrounded by (Argentine) war veterans," he said. Veterans were on a visit to the islands and some took part in the marathon.
Government Sports secretary Claudio Morresi told Reuters in an interview last month; "The Argentine delegation will travel to London with the conviction in their minds and hearts that the Malvinas are Argentine but all they will be going to London to do is take part in the sporting event."