The ad was shown during halftime of Sunday's soccer game between Boca Juniors and Rafaela. The ad says it was released by the Argentine presidency.
The spot first aired Wednesday and has run several times since the International Olympic Committee denounced it Friday. The IOC warned that the Olympics should not be used "to raise political issues."
The ad shows men's field hockey captain Fernando Zylberberg training for the games by running through the islands' capital of Stanley. In the background is a British pub and other national symbols. The ad says: "To compete on English soil, we train on Argentine soil."
Several reports over the weekend, quoting unidentified government officials, said the ad will run several times more. Argentina's ambassador to Britain, Alicia Castro, told an Argentine newspaper the ad was done without malice.
"This is not meant to be a provocation," Castro, told the daily El Tribuno. "Nobody has had the intention to offend."
On Friday, the IOC said it wrote to the Argentine Olympic Committee.
"The Olympic Games should not be a forum to raise political issues and the IOC regrets any attempts to use the spotlight of the games for that end," the IOC said in a statement to The Associated Press.
Gerardo Werthein, president of the Argentine Olympic Committee, acknowledged the games "are not a platform to discuss politics."
Werthein could be put on the spot. The capital of Buenos Aires is one of six cities bidding to host the 2018 Summer Youth Olympics. The host city will be chosen in July 2013.
The Argentina government and President Cristina Fernandez have used the issue of the Falklands — known in Argentina as Las Malvinas — to stir national pride and say they want Britain to hold talks over the sovereignty of the South Atlantic islands. Britain has said the residents of the islands should have the last word. They have overwhelmingly said they want to remain British.
Argentine Foreign Minister Hector Timerman increased the rhetoric Sunday after British Defence Secretary Philip Hammond said Argentina should apologize for the ad.
"Mr. Hammond should know that the world is safer when we use creativity, rather than bombing civilian populations in sovereign countries," Timerman said. He called Hammond "an adversary to fear."
The ad was produced by the British-owned advertising agency Young & Rubicam, which apologized for the ad created in Argentina. Martin Mercado, the creative managing director of Young & Rubicam in Argentina, said the ad was designed for home consumption.
"It was a message for the country, for Argentines," Mercado said. "It was not for the outside."
Reports have circulated that Argentine athletes in London might attempt to wear T-shirts raising the issue. An Argentine legislator suggested months ago that Argentine athletes should wear a logo on their uniforms with images of the islands and, perhaps, carry the message: "Las Malvinas son Argentinas" (The Falklands are Argentine).
Follow Stephen Wade at https://twitter.com/StephenWadeAP