Mo'men Fawwaz Kmeil, 20, was shot on Tuesday as he tried to escape a standoff between Palestinian forces and local armed men in a cafe in the town of Qabatya near Jenin, residents said.
Palestinian forces said in a statement that the man was killed when an "outlawed group" opened fire on the security men.
The killing came after hundreds of Palestinian national security troops and presidential guards were deployed in the West Bank city of Jenin on Saturday.
Force deployed
The deployment is part of an operation backed by Washington to show the Palestinian Authority (PA) can curb the activities of Palestinian armed groups - a key Israeli condition for Palestinian statehood.
It is the second-biggest Palestinian security campaign in a major West Bank city following a similar mission in Nablus late last year.
The campaign, which is being carried out in co-ordination with Israel, saw about 600 men deployed in the city.
Another 150 men already in Jenin have also taken part in the campaign.
The force have entered Jenin's refugee camp and other areas that have been off-limits to Palestinian forces.
Commanders of the force say they are determined to impose law and order and confiscate illegal weapons.
Powerful clans such as the Kmeils have long-ruled Qabatya
and the incident could create tension between the groups and the new force.
The Jenin campaign will cover 50 villages and is supposed to last three months.