An Israeli military source said on Thursday that troops opened fire after the fighter had attacked an Israeli checkpoint with grenades and gunfire and wounded two soldiers.
Jewish settlers in occupied Gaza said a Palestinian passerby was also wounded in the incident at the Orchan junction, north of an illegal colony.
The soldiers were the first Israeli casualties in nearly two weeks following the deployment of Palestinian police in some parts of Gaza, under orders from the recently elected Palestinian President Mahmud Abbas.
Dozens of Palestinians have been killed, wounded and arrested in the same period of time.
In a separate incident, a second resistance fighter opened fire on colonists near the Eshkolot settlement south of the West Bank city of Hebron, wounding two Israelis, one of them seriously, a military source said.
The army would not say whether those hurt in the West Bank
were soldiers or civilians.
The attacks come hours after officials on both sides had expressed their hopes that an 8 February summit in Egypt might cement a de facto truce in the Palestinian territories.