An Israeli military source said soldiers exchanged fire with gunmen during a raid to arrest wanted armed men near Nablus on Friday.
Medics said a Palestinian gunman was killed and another was arrested in the raid.
Two Israeli soldiers were also wounded in the gun battle.
Earlier on Friday, the Israeli military launched three air raids against targets in the Gaza Strip.
An Israeli military spokesman said: "Our helicopters launched three attacks.
"Two targeted two offices at Bait Lahya (north) where activists of the al-Aqsa Martyrs' Brigades were meeting to plan rocket strikes against Israel, and another attack was against a helicopter pad inside Gaza City."
The Brigades are the armed offshoot of the Fatah movement of Mahmoud Abbas, the Palestinian president, who arrived in Gaza City on Thursday to meet senior members of the new Hamas-led government.
The Israeli spokesman said Palestinian fighters had launched six homemade rockets against southern Israel on Thursday.
One hit the village of Sderot without causing any damage, while another hit a factory at Ashakelon, sparking a fire.