The probe will be carried out in coordination with Jordanian authorities, the army said.
The shooting death of judge Raed Zeiter, who is of Palestinian origin, caused a furor in Jordan, which has a 1994 peace treaty with Israel, and strained the two neighbors relations.
Israeli troops killed Zeiter, 38, at a border crossing between the West Bank and Jordan, saying he had attacked them and tried to take one of their weapons.
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The incident led to protests against Israel in the kingdom, and Jordanian politicians called for a nullification of the peace accord and the expulsion of Israel's ambassador to the kingdom, while others burnt an Israeli flag at the Jordanian parliament.
"The Israeli army prosecutor's office has decided to open a new investigation into this incident," an army spokeswoman told AFP Monday.
"An investigation was carried out immediately after the incident in the form of witnesses being questioned… (but) on the instructions of the political leadership, the military command of the Central Region (covering the West Bank) has decided to open a new probe."
The IDF initially said Judge Raed Zeiter was shot dead on after attacking a soldier at the terminal, suffocating him and trying to snatch his weapons. An army investigation found Zeiter ignored calls to stop, and continued attacking soldiers at the scene with an iron rod even after he was shot in his leg.
But his family, witnesses, and Palestinian rights groups dispute the army's account, saying he was killed during a row with the soldiers.