Gerardo Pollicita inherited the case from Alberto Nisman, who was found dead in mysterious circumstances.
Cristina Fernandez de Kirchner denies the allegations, with the government calling the probe an “anti-democratic attack”.
The attack on a Jewish centre killed 85 people. Iran also denies involvement.
Gerardo Pollicita’s move mean the judge will have to decide whether to authorize new investigations to prove the president’s alleged involvement.
If the prosecutor and the judge agree that there are enough elements to prove Cristina Fernandez de Kirchner committed a crime, she could face prosecution and be charged.
Before his death, Alberto Nisman had published a report on the attack on the Amia Jewish centre.
He alleged that the president and others had conspired to protect Iranian suspects in the bombing case in exchange for favorable deals on oil and other goods.
Alberto Nisman was found shot in the head in January, hours before he was due to give evidence to Congress.
Cristina Fernandez de Kirchner’s cabinet chief, Jorge Capitanich, accused the courts of trying to stage a “judicial coup” by pursuing the investigation, the AFP reported.
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