The advertisement says the athlete is preparing for London 2012 on "Argentine soil", was the brainchild of WPP-owned agency Young & Rubicam (Y&R).
Zylberberg is seen running in the Falklands capital, Port Stanley, and exercising on the island's Great War Memorial, which honours British sailors who died in the First World War.
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In an interview with Al Jazeera English, Olympic hopeful Zylberberg said that the advert was supposed to convey his country's feeling over the islands.
"The message is that to every Argentine the islands belong to Argentina. To me to be training in any other province or to do it over the islands is the same," he told the broadcaster.
"But when we were there we did not say that we were doing an advertisement but we were not hiding. In fact people helped us."
He added that he had been told by the agency while making the advert there was no buyer and that they would seek one after it had been made.
He was only told two months later "there was a chance that the Argentine government could be interested", he said.
Sorrell, the head of communications giant WPP, branded the television clip "totally unacceptable" and professed himself "appalled and embarrassed".
Y&R said it had asked the Argentinian government to pull the spot, accusing its creators of behaving "in a manner that is unacceptable to our company".
The advert, reportedly bought by the government and broadcast after being rejected by various companies, calls the islands by their Argentinian name, the Malvinas, and carries the tagline: "To compete on British soil, we train on Argentinian soil."
The advert follows months of political bickering between London and Buenos Aires on the issue of the disputed South Atlantic islands.
The Argentine president has been attempting to reassert Argentina's claim to the British overseas territory, but the British government says it will not discuss the issue without the agreement of the Falkland Islanders.

