The Israeli military said its forces had come under heavy Palestinian fire on Monday while seeking the arrest of security suspects in Jenin and had returned fire at the gunmen.
Palestinian President Mahmoud Abbas's Fatah party identified the officer as Ashraf Sheikh Ibrahim, saying he had died "as he confronted the aggression and the occupation's storming of the city of Jenin".
Al-Aqsa Martyrs Brigade militant group, associated with Fatah, claimed him as a member.
In another part of the West Bank on Monday, Jewish settlers inaugurated a seminary in a settler outpost, drawing Palestinian condemnation.
In a video posted on social media, settler leader Yossi Dagan recited a Jewish benediction at the entrance to the Homesh seminary school, a large white prefabricated shack at the top of a West Bank hill.
"With God's help ... there will be many more new settlements in northern Samaria," he said, referring to the West Bank by its biblical name. The new school was moved off privately owned Palestinian land to a new spot on the same hilltop around 150 metres away.
Last week, the US State Department had warned Israel against establishing a permanent presence in the Homesh outpost in the northern West Bank, which it said "according to Israeli law was illegally built on private Palestinian land".
Yesh Din, an Israeli rights group representing some of the Palestinian landowners, said that in its new location the seminary obstructs access to their property.
US-led peace talks aimed at establishing a Palestinian state in the West Bank, East Jerusalem and Gaza broke down in 2014 and show little sign of revival, and Israeli-Palestinian violence has escalated over the past year.
Most countries deem Israel's settlements illegal - a view Israel disputes. Palestinians say they eat away at the land they want for a future state and cite growing violence by settlers.
Abbas said Homesh must be removed. "Statements of condemnation are no longer enough in the face of the (Israeli) extremist right-wing government," said his spokesman Nabil Abu Rudeineh.
In a bid to quell international concern, Prime Minister Benjamin Netanyahu has said that Israel has no intention of building any new settlements as his nationalist-religious government has vowed to bolster existing ones.
Spokespeople for Netanyahu, Defence Minister Yoav Gallant and Finance Minister Bezalel Smotrich did not immediately respond to Reuters requests for comment on whether any of them had authorised the establishment of the new Homesh seminary.
"I think there are times when it's preferable to talk less and do more," Smotrich told reporters at a meeting of his pro-settler Jewish Zionism party, when asked who was behind the decision on Homesh.
Last week, Smotrich, who holds some West Bank powers, said Homesh had been officially added to settlement council land in order to work out a new building plan for the seminary school.
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