According to his own statements, the Nahal soldier was removed from duty for assaulting a superior officer, but initial reports that he was suspended for cocking his weapon at a Palestinian in Hebron sparked an aggressive Facebook drive for his reinstatement.
Gantz addressed the affair at the weekly General Staff meeting, promising to investigate the Hebron incident: "We will look into the events that led to the incident and draw the necessary conclusions."
The IDF Chief of Staff said the unprecedented online campaign of dissent "raised issues of ethics in the military, which we must deal with on every level."
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Israeli troops, covering their faces to avoid punishment, have mounted an online campaign in support of a soldier whom they believe was jailed for pointing his gun at Palestinians who were arguing with him.
The massive outpouring of support on Facebook was described on Thursday in front-page reports in the Israeli media as a sign of soldiers' frustrations over their service in Palestinian territory, where their actions are often under scrutiny by journalists and pro-Palestinian activists with cameras.
The online furor erupted when the soldier, identified only as "David from the Nahal brigade", was sentenced to 20 days in military prison after he was shown in a video clip loading and pointing his rifle at Palestinian youths who approached him during guard duty and argued with him.
The Israeli military issued a statement saying the soldier's punishment was for unruly behavior towards superior officers and not connected to the incident, which was posted on YouTube on Sunday by Palestinian activists and took place in the West Bank city of Hebron.
Nonetheless, troops rallied behind David. A Facebook page – "I also back David from Nahal" – showed hundreds of photographs, many of them of men and women soldiers in uniform who held placards in front of their faces with messages of support.
Another Facebook support page had more than 80,000 "likes" on Thursday.
In the past, the army has punished troops for posting material on social media, which has included, most famously, women soldiers posing in their underwear while holding guns.
Violence in the West Bank has decreased since a Palestinian uprising ended in 2006, but Palestinians and human rights groups regularly complain of heavy-handed treatment by the Israeli military.
Breaking the Silence, an Israeli human rights group that publishes soldiers' accounts of their service in territory Israel occupied in a 1967 war, said the confrontation depicted in the "David" video was "far from unusual".
Economy Minister Naftali Bennett, who heads a far-right party, also came out, on his Facebook page, in support of David, saying the soldier "did the right thing".
"This isn't a reality show. It is a complicated and dangerous situation with which Israeli combat troops must deal on a day-by-day basis," he wrote.
Reuters contributed to this report.