More than 100 Palestinians have been killed in clashes since the beginning of the year, most of them since March.
An Israeli military statement said troops came under heavy fire during an operation in the city of Jenin, in which an armed operative of the Hamas group and two other people were arrested. It said troops returned fire and "hits were identified".
The Jenin Brigade, an umbrella group of different armed factions, said one of its members had been killed.
Atta Abu Rumeileh, a leader for the Fatah group in Jenin, told the media that the other man killed was a doctor and Fatah member who participated in the fighting.
The cities of Jenin and Nablus, both home to sprawling refugee camps, have been at the centre of violence.
In a separate incident late Friday, the Israeli military said it responded with live fire to a shooting attack at a settlement near the West Bank city of Ramallah that left an Israeli civilian lightly wounded. It said soldiers killed one assailant and were searching for other suspects.
The Palestinian Health Ministry said a 23-year-old was killed by Israeli gunfire near Ramallah. It was unclear whether he was linked to any group.
More than 100 Palestinians have been killed in clashes since the beginning of the year, most of them since March when the Israeli army launched a crackdown in the West Bank following a series of attacks by Palestinians in Israel.
Nabil Abu Rudeineh, the Palestinian president's spokesperson, said Israel had "crossed all red lines" and the Palestinian Authority would not allow the situation to continue.
The cities of Jenin and Nablus, both home to sprawling refugee camps, have been at the centre of violence. But there have been incidents in other parts of the West Bank and East Jerusalem, with two Israeli soldiers killed this week.
Roads into Nablus were closed during the week with heavy security checks and on Friday the military said troops carried out an operation in the city and arrested two people suspected of firing on them.
Both the Israeli military and Palestinian officials say groups of young armed men in Nablus and Jenin, often only loosely associated with established political movements, have been at the forefront of clashes.
There have also been repeated clashes between Israeli settlers in the West Bank and Palestinians.
Israel captured the West Bank, East Jerusalem and Gaza — areas that Palestinians want for an independent state — in a 1967 Middle East war.
The Israeli military said Palestinians had started "a violent riot" near the town of Qarawet Bani Hassan on Saturday and soldiers who had been operating there opened fire.
Israel and Palestinians unleashed salvos of fire for a fifth day on Saturday, with the Islamic Jihad group launching dozens more rockets and the Israeli military pounding targets inside the Gaza Strip.
The number of Palestinians killed in the war passed 10,300, including more than 4,200 children, the Hamas-run Health Ministry in Gaza said on Tuesday.
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