The retired colonel with extreme views coined the term "smile-enjoy-kill", which was an order to his troops to fire at fleeing Palestinians.
The deaths bring to 80 the number of Palestinians killed since the start of the year, as Israel has stepped up arrest raids in the West Bank.
Israeli troops shoot dead three Palestinians in Jaba town, and a 14-year-old boy succumbs to wounds sustained on Tuesday from Israeli bullets in Jenin city, says Palestine's Health Ministry.
Shooting comes amid rising tensions across the occupied West Bank following an Israeli military raid in Nablus in which 11 Palestinians were killed.
It is second such attack which comes days after Israeli raid in West Bank's Jenin refugee camp that killed 10 Palestinians.
The Palestinian Health Ministry names the two young men killed as Ezzedine Bassem Hamamra, 24, and Amjad Adnan Khaliliya, 23.
Palestinians push back against Israeli police claims that 22-year-old Ammar Mufleh Adili was shot dead in self-defence, saying there is no justification.
Israeli warplanes target Gaza following a deadly week of escalated violence in the occupied West Bank, where 10 Palestinians have been killed by Israeli forces.
The body of 17-year-old Haitham Mubarak has been handed over to Palestinian authorities two months after he was shot dead by the Israeli army in the occupied West Bank, where military raids and expulsions against Palestinians continue.
Settler violence has a history of targeting the Israeli security establishment, which willingly turns a blind eye to it.
The Israel military said on Twitter that the incident took place near the town of Kiryat Arbaas when the alleged attacker "carried out a stabbing attack, injuring a soldier".
About 150,000 Palestinians have gathered at Al Aqsa Mosque in defiance of Israel's visitation restrictions and violent attacks on worshippers during the holy month.
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