Israel's army chief has reduced a jail sentence handed down earlier against a former soldier convicted of killing an alleged Palestinian attacker who had been injured and unarmed at the time, local media reported on Wednesday.

In a letter to former soldier Elor Azaria, Army Chief-of-Staff Gadi Eisenkot announced the decision to reduce Azaria's sentence by four months despite his stated lack of remorse, according to the Times of Israel.

In June, an Israeli military court rejected Azaria's appeal against his conviction while also rejecting a request by military prosecutors to extend his 18-month jail sentence.

The case had rocked Israel's government last year, leading to the departure of Defense Minister Moshe Yaalon, who had supported the military's decision to investigate Azaria.

Prime Minister Benjamin Netanyahu, for his part, along with others in his right-wing coalition, had expressed sympathy for the convicted soldier.

The case came to light early last year after a video emerged showing Azaria fatally shooting a young Palestinian man in the head at close range -- Abdel-Fattah al-Sharif -- following an alleged attack in the occupied West Bank city of Hebron.