
A ruling on the request by Elor Azaria was expected in the coming days, an army spokeswoman said.
Azaria was convicted of manslaughter last year for shooting Abdul Fatah al-Sharif in the head in March 2016, as the Palestinian lay on the ground wounded after stabbing a soldier.
Azaria was sentenced to 18 months in prison, but Israel's Chief of Staff General Gadi Eisenkot later reduced the term by four months.
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The shooting in the occupied West Bank city of Hebron was caught on video by a human rights group and spread widely online.
It showed 21-year-old Sharif lying wounded on the ground, shot along with another Palestinian after the stabbing attack, according to the army.
Azaria then shot him in the head without any apparent provocation.
The Israeli soldier said he feared Sharif had been wearing an explosive belt and could have blown himself up, a claim judges rejected.
In November, Israeli President Reuven Rivlin on Sunday formally rejected a request to pardon Azaria.
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According to media reports, the military prosecutor would not be opposed to reducing Azaria's sentence by one third, which could see him walk free on May 10.
But his lawyer Yoram Sheftel is reportedly set to plead for his immediate release based on his good behaviour.
The months-long trial of Azaria captivated Israel and highlighted deep divisions in public opinion.
His sentence was condemned by right-wing politicians as too harsh and labelled too lenient by Palestinians and rights groups.
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