The first attack took place in the centre of the flashpoint city of Hebron, where one victim was seriously injured and another slightly hurt, police spokesman Micky Rosenfeld said.
The army said one of the victims was a soldier who was stabbed by a Palestinian he had stopped for an identity check.
The stabbed civilian is the son of former Israeli lawmaker Orit Struck of the religious and nationalist Jewish Home party, the politician told Israeli radio.
Palestinian security sources identified the attacker as Abed al-Rahman Maswada, 21.
He was said to be the cousin of another Palestinian attacker shot dead in Hebron on Monday after stabbing an Israeli.
Hebron, in the southern West Bank, has been a flashpoint in more than two months of Palestinian knife, gun and car-ramming attacks.
Tensions between Israeli settlers living under heavy military guard in the heart of the city and Palestinian residents have been high.
Later in the evening, assailants shot at a car near the West Bank town of Tulkarem, wounding two Israelis, the army said.
Since October 1, almost daily attacks and clashes between Palestinians and Israeli soldiers have killed 113 on the Palestinian side, 17 Israelis, an American and an Eritrean.
Many of the Palestinians killed have been attackers, while others have been shot dead by Israeli security forces during clashes.
Young Palestinians have grown frustrated with Israel's occupation and the complete lack of progress in peace efforts in addition to their own fractured leadership.
Three Palestinians were wounded by gunfire while tear gas was also used, Palestinian police and witnesses said.
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