Wednesday's incident came against a background of escalation in Israeli-Palestinian tensions.
On Tuesday, an Israeli air strike aimed at fighters killed three children in a crowded refugee camp in the Gaza Strip.
Medics at a Nablus hospital said Daud Qatuni, 25, a member of al-Aqsa Martyrs' Brigades, an armed wing of the Fatah movement of the Palestinian president, had died of injuries sustained when he was shot in the head by Israeli soldiers.
Palestinian security sources said an exchange of gunfire took place in the Ain Bait Ilma refugee camp, near Nablus, in the early hours of Wednesday.
Relatives mourn over the body
of Daud Qatuni, aged 25
The Israeli army said troops searching for wanted fighters had come under fire and shot and killed Qatuni, who they said was armed.
Aljazeera reported that clashes occurred near the old city when Israeli forces tried to help a special military unit to leave the area.
The unit had earlier entered the city in to arrest some Palestinians, but could not get out, the correspondent said.
Gaza crossing closed
The Israeli army also deployed its forces east of Bait Hanun and Bait Lahya towns, in the northern Gaza Strip on Wednesday, Wail al-Dahduh, Aljazeera's correspondent in Gaza, reported.
The Gaza Strip's main gateway to the outside world was closed on Wednesday after an Israeli security alert in the area, European monitors at the crossing said.
Nigel Milverton, a spokesman for the monitors, said the monitors at the Rafah crossing between Gaza and Egypt were not able to reach Rafah crossing because Israel had closed a different crossing nearby due to a security alert and would not let them through.
Hamas has criticised the closing
of the Rafah border crossing
The Israeli army confirmed that it had closed the crossing because of fears of an attack.
Sami Abu Zuhri, a spokesman for Hamas, said the closure was to prevent the group bringing cash through Rafah to get around a boycott on the three-month-old government.
"We have information some Palestinian officials urged European monitors to do this to prevent Hamas officials bringing money through Rafah to resolve our financial crisis," Abu Zuhri said.
A spokesman for the EU monitors dismissed the suggestion.
"The only reason our deployment has been delayed is because of the security alert," the spokesman said.