The Israelis were searching for Rashid Zakarna, a wanted fighter who exchanged fire with troops before he was shot and killed in the northern town of Qabatiya, the hospital officials said on Thursday.
Witnesses said dozens of troops surrounded the building where the fighters had holed up before the shootout erupted.
Two unarmed Palestinians were killed in the exchange of fire, and 11 were injured, officials said
The Israeli army confirmed that troops were making arrests in Qabatiya and that a shootout had erupted.
Zakarna, a local leader of the al-Aqsa Martyrs Brigades, was wanted by Israel, and had been held in an Israeli prison in the 1990s, the group said.
The group is loosely linked to the Fatah party of Mahmoud Abbas, the president.
Meanwhile, a strike over unpaid salaries by civil servants has entered its sixth day amid pro and anti-strike demonstrations.