Israeli Prime Minister Naftali Bennett said every effort was being made to catch those responsible.
The incident follows a recent spike in Palestinian attacks on Israelis.
The Israeli military said the men were ambushed as their vehicle left a religious seminary at Homesh, a so-called outpost settlement, one of a type built without government authorisation.
Israeli settlements on territory occupied since the 1967 Middle East war are considered illegal under international law, though Israel disputes this. Palestinians claim the land for a hoped-for independent state.
Following the shooting, homes in two Palestinian villages were attacked with stones, one was set on fire and two residents were beaten in what locals say were revenge attacks by Israeli settlers.
Hundreds of mourners gathered at Homesh on Friday morning, where the head of the seminary, Rabbi Elishama Cohen, declared: “[We] will say loudly and clearly that this place is fully ours,” the Times of Israel reported.
Mr Bennett denounced what he called an “horrific” attack, vowing that “security forces will get their hands on the terrorists very soon and we’ll ensure that justice is served”.
The Palestinian militant group Hamas, which governs the Gaza Strip, praised the shooting, calling it part of a “legitimate struggle”.
The Israeli military deployed three additional battalions to the West Bank as security forces searched for the attackers. Several Palestinians were arrested overnight in connection with the investigation, Israeli and Palestinian media say.
The shooting follows a spate of attacks on Israeli Jews in recent weeks.
Last week in Jerusalem, a 14-year-old Palestinian girl was arrested on suspicion of stabbing her Jewish neighbour. Days earlier, a Palestinian stabbed a Jewish man in the street before being shot dead by Border Police.
Last month, a Hamas gunman killed an Israeli and wounded three others in Jerusalem’s Old City before being shot dead.