Abed Shaker el-Wazir, the 70-year-old man, was apparently hit by a stray Israeli bullet, a Palestinian official said.
The other Palestinian killed was a local leader of the al-Aqsa Martyrs Brigades group, which is linked to the Fatah faction of Mahmoud Abbas, the Palestinian president.
Al Jazeera's David Chater in Nablus said "there have been a lot of exchanges of automatic fire and explosions" and that the Israelis were also using tear gas and stun grenades during the operation.
Stone-throwing
Two members of the al-Aqsa Martyrs Brigades were also wounded in the firefight, which began after around 40 Israeli jeeps and three bulldozers entered Nablus early on Tuesday.
Several Palestinian fighters were also arrested during the raid.
Witnesses said Israeli soldiers later opened fire in order to disperse Palestinian stone throwers.
Five Palestinians were wounded, including Alaa Badarneh, a photographer for the European Press Agency, who was hit by a rubber bullet in the back, medics said.
The Israeli military often carries out raids on Nablus in what it says are searches for wanted Palestinian fighters.