One was killed during an army raid in the Qalandia refugee camp.
The Israeli military said it had been conducting arrests and confiscating weapons throughout the West Bank.
At one location in Qalandia, it said, soldiers came under attack by locals and responded with dispersal methods and live fire.
Later in the area of Jenin, where witnesses reported a firefight, Israeli forces killed two Palestinians, the Palestinian Health Ministry said.
The Israeli army said troops there apprehended a suspect over "involvement in terrorist activity and planning attacks".
Soldiers opened fire, it said, after being shot at and a "violent riot" erupted.
The West Bank, among areas where Palestinians seek a state, has had a surge of violence since Israel stepped up the operations in response to a series of street attacks in its cities last year.
In the first two weeks of 2023, eight Palestinians have been killed in the raids, including three teenagers, according to Palestinian officials.
No Israeli soldiers have been killed in the operations.
Separately, on Wednesday, in the southern West Bank, a Palestinian stabbed a Jewish settler at a farm and was shot dead, Yochai Damri, the head of local settlements, told Israel's Army Radio.
It was not clear whether the wounded settler or someone else fired the shots, he said.
Israel says the raids are a security measure targeting suspected militants.
Palestinians consider the raids a form of collective punishment and say they are fighting against decades of Israeli occupation.
Addressing a United Nations Security Council meeting on the rule of law on Thursday, Secretary-General Antonio Guterres said 2022 had been a deadly year for both Palestinians and Israelis and condemned all "unlawful killings and acts by extremists".
"At the same time, the expansion of settlements by Israel, as well as home demolitions and evictions, are driving anger and despair," Guterres said.
"I am also very concerned by the unilateral initiatives that we have seen in recent days."
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