|Argentine President Cristina Fernandez de Kirchner|
Prosecutor Gerardo Pollicita inherited the case from Alberto Nisman, who was found dead in mysterious circumstances.
The president denies the allegations, with the government calling the probe an "anti-democratic attack".
The attack on a Jewish centre killed 85 people. Iran denies being involved.
The latest prosecutor's move means the judge will have to decide whether to authorise new investigations to prove the president's alleged involvement.
The investigation looks at the 1994 bombing of a Jewish centre in Buenos Aires
If the prosecutor and the judge agree that there are enough elements to prove Ms Fernandez committed a crime, she could face prosecution and be charged.
Analysis: Ignacio de los Reyes, BBC News, Argentina
Although this was an expected move, it could not have come at a worse time for the Argentine president.
Cristina Fernandez de Kirchner was already facing criticism for the way she has been managing the Nisman case, which has become the worst crisis of her political career so far.
Now she will also face pressure from the judiciary, which is demanding an unprecedented investigation into a sitting president - one that could end up with an impeachment-like process if she is found guilty.
Meanwhile, prosecutors are calling for a massive protest on the streets of Buenos Aires next week in what is expected to become the largest anti-government march in recent years.
Opposition leaders, unions and even the Catholic Church are joining calls for a fair and independent investigation into a death that has shocked this nation.
He alleged that the president and others had conspired to protect Iranian suspects in the bombing case in exchange for favourable deals on oil and other goods.
Mr Nisman was found shot in the head in January, hours before he was due to give evidence to a congressional committee.
The president suggested he may have been manipulated into killing himself by rogue security agents in an attempt to discredit her.
A document written by Mr Nisman's successor said there was enough evidence to go ahead with the case.
"An investigation will be initiated with an eye toward substantiating... the accusations and whether those responsible can be held criminally responsible," Mr Pollicita wrote.
President Fernandez's cabinet chief, Jorge Capitanich, accused the courts of trying to stage a "judicial coup" by pursuing the investigation.
Anibal Fernandez, a spokesman for the presidency, said moving the case forward was a "clear manoeuvre to destabilise democracy''.
|A team of police investigators arrive at Le Parc Tower where the late prosecutor|
Alberto Nisman was found dead
January 14: Nisman files a 300-page report accusing President Fernandez of colluding to shield Iranian suspects.
January 18: Nisman is found dead at his apartment
January 22: President Fernandez says she is not convinced his death was suicide
January 27: The president announces she is disbanding Argentina's intelligence agency following the death
February 10: Experts find DNA from an unidentified person in Nisman's apartment
February 13: Prosecutors say they are pursuing Nisman's claims