Residents of the village of Rajub say that in the small hours of Sunday morning soldiers fired at a house on the outskirts of the village, where 20-year-old Fawzi Dwaikat was standing guard with a rifle after arson attacks on the family's cars.
Dwaikat and his 50-year-old mother Nawal were killed by shots from the soldiers who apparently believed they had come across a hideout, neighbours said.
The military said initial reports indicated that an army patrol had been shot at from a house in the village and returned fire, killing two people and wounding three. There was no immediate confirmation of the age or sex of the dead, but the army said arms and ammunition were found in the building.
On Saturday, armed Palestinians, including off-duty policemen, temporarily halted traffic on two major roads in the Gaza Strip amid mounting chaos ahead of the 25 January Palestinian elections.
With the violence reinforcing Hamas' prospects in the legislative election, US officials warned that millions of dollars of aid could be in jeopardy if the Islamic group joins the Palestinian government.
Palestinian leader Mahmoud Abbas said Hamas participation in the government is not a US affair.