The two Iranian nationals were arrested on Saturday morning in Buenos Aires.
The man, aged 27, identified himself as Sajjad Naserani and claimed he was a photographer. The woman, 31, presented herself as Mahsoreh Sabzali and said she was an engineer and an architect.
The forgeries are blatantly amateurish, with many clear typos in Hebrew.
Police cordoned off a 40-block area to contain the suspects, who were found and detained in an apartment hotel in the Abasto area of the city.
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The suspects told investigators that they traveled via Turkey to Greece. From there they went on to Spain, where they likely obtained their forged Israeli passports. Using the documents, the couple arrived in Argentina through the Ezeiza international airport on Tuesday.
Interpol confirmed that the passports used by the Iranians do not correspond to real Israelis. According to Clarin, after contacting the Israeli authorities, it was confirmed that the passports' ID number belonged to two other Israelis of French descent.
This is not the first time that Iranians have attempted to enter Argentina clandestinely. A similar incident took place a few days before last year's G-20 summit, when two Iranian men were arrested after they entered the country via Bolivia using forged passports. They were found with a small weapons arsenal, Arabic-language credentials and the image of a Hezbollah flag.
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