A member of the Israeli security forces outside Damascus Gate in Jerusalem's Old City on June 16, 2017 following an attack.
Speaking at the opening of the weekly cabinet meeting in Jerusalem, Netanyahu noted that rather than condemn the Palestinians who killed Border Police officer Hadas Malka, PA President Mahmoud Abbas's Fatah movement "issued a statement in which it condemned Border Police officers for killing the terrorists and praised the murderers as heroes".
At one location, two Palestinians were shot dead after opening fire at a group of Israeli police officers.
In the other incident, two attackers armed with a knife and a gun were shot by an Israeli police officer with at least two bystanders also reportedly hurt.
Three other people were shot and injured at the scene of the gunfire, several blocks away.
The Israeli forces said the assailants appeared to have acted independently, like numerous attackers in a wave of unrest that has rocked Israel and the occupied territories since October 2015. However, there have been a string of recent attacks near the Old City. Earlier, Prime Minister Benjamin Netanyahu said that preparations are underway to destroy the homes of the Palestinian attackers and tighten security at the entrance to the Old City, home to sensitive holy sites sacred to Jews, Muslims and Christians. In that time, some 250 Palestinians were killed by Israeli fire.
But the claim, which came with the Islamists facing defeat in their Iraq and Syria bastions, was swiftly dismissed by Palestinian militant groups.More news: Iran calls missile attack on Syria militants a wider warning
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Israeli soldiers invaded, late on Friday at night, Deir Abu Mashal village, west of Ramallah, after besieging it for several hours, leading to clashes with local youngsters, before shooting three Palestinians with live rounds, and causing many to suffer the effects of teargas inhalation.
Most of the attacks have been carried out by "lone wolves", some only in their teens, and Israel has dubbed the violence "popular terrorism".
The attack took place as Muslims marked the end of the third Friday of the fasting month of Ramadan, during which tens of thousands of Palestinians from east Jerusalem and the West Bank attended prayers at the nearby Al-Aqsa mosque compound, Islam's third-holiest site.
ISIS claimed the attack shortly after it occurred, but Hamas rejected it Saturday.
The Palestinian Center for Human Rights (PCHR) strongly condemned these measures and stressed they fall within the collective punishment policy which is prohibited in the worldwide human rights law.
Palestinians say it stems from anger over decades of Israeli rule in territories they claim for their future state.