Two Palestinians, a father and his son, were killed on Saturday during clashes between Israel Defense Forces troops and gunmen in the Beit Hanoun neighborhood in the northern Gaza Strip.
In another incident, a Palestinian was killed near the Kissufim border crossing in south Gaza.
The army said a man was spotted acting suspiciously near Kissufim and opened fire when he ignored their instructions to stop.
Palestinian sources said the man has not been identified and it remains unclear whether he was armed.
In the first incident, witnesses said Israeli troops backed by helicopters entered the northern Gaza town of Beit Hanoun and engaged in heavy clashes with Palestinian gunmen there.
A resident, Younis Abu Odah, told local media bullets fired during the gunfight came through his house and killed his 54-year-old father and 27-year-old brother, while also wounding two of his sisters.
It was unclear whether the bullets were fired by Israeli forces or Palestinian gunmen. Medics have so far been unable to reach the area to confirm any deaths or evacuate the wounded due to the heavy gunfire.
At the same time, Israeli air strikes in a nearby part of Beit Hanoun wounded three Palestinians, two of them children, with shrapnel, medics said.
Also on Saturday, IDF forces operating in Beit Hanoun apprehended two Hamas activists who were involved in planning and carrying out rocket attacks against Israel, the army said.
IDF forces have apprehended a number of Hamas activists in Gaza in recent weeks with the aim of interrogating detainees and exposing plots to carry out terror attacks against Israeli targets; a tunnel dug with the purpose of carrying out an attack at the Karni crossing was uncovered earlier in the week in the Sajaiya neighborhood in Gaza.
Israel began an offensive in Gaza in late June, after gunmen abducted Corporal Gilad Shalit in
a cross-border raid.
The eight-week offensive is designed to recover Shalit and also to prevent Palestinian gunmen from firing makeshift rockets from northern Gaza into Israel.
Hanan Greenberg and Reuters contributed to the report