The incident has already begun to influence the ongoing election campaign, with Netanyahu - who has built his campaign on the promise of security - saying that his Likud party would cancel campaign events which had been set for Friday morning.
Speaking later from the scene, Netanyahu said that the military would "demolish this place and completely transform it," referring to the Hebron neighbourhood where the attackers are said to have come from.
It is common for Israeli forces to demolish the homes of Palestinians who are suspected of carrying out attacks on Israelis - a practice Israeli rights groups have criticised as collective punishment.
Netanyahu likened his plans to previous operations in West Bank refugee camps where residential buildings were demolished and thousands were displaced.
He also said he had reviewed plans for the largest military operation in the West Bank in decades - though did not say when it could be carried out.
He added that he had imposed cordons around the city of Hebron - which has around 200,000 residents - and the nearby city of Halhul.
Netanyahu's far-right Finance Minister Bezalel Smotrich called for Israel to launch a campaign in the West Bank "exactly like in Gaza or Lebanon," while far-right National Security Minister Itamar Ben Gvir called for Israel to dismantle the Palestinian Authority.
On Thursday, Foreign Minister Israel Katz accused opposition leaders of undermining the government by criticising Netanyahu's warnings of an attack ahead of the election, saying they would be "responsible" for any future attack on the country.
Opposition chiefs, including frontrunner Gadi Eisenkot and former Prime Minister Naftali Bennett, offered their condolences to the families of the killed troops and praised those who killed the attackers.
The Israeli military said it had found a large quantity of ammunition in the attackers' vehicle, and that they believe the gunmen had intended to carry out a much larger attack on the nearby Route 35, but ran into the checkpoint - so instead decided to open fire there.
At least 96 Palestinians have been killed by Israeli forces or settlers in the West Bank since the start of the year, according to the UN.
Four Israelis, both security forces and civilians, have been killed by Palestinians there over the same period, the UN says - not including those killed in Friday's attack.