The army said a group of six Palestinians, in the early hours of Monday morning, approached a fence in the northern Gaza Strip that separates the occupied Palestinian area from Israel.
The army claimed that one of them was captured when four of the group apparently entered Israel. It was possible the group wanted to enter Israel to find work, the army said.
Police and soldiers, meanwhile, searched for the other three Palestinians, setting up impromptu checkpoints and roadblocks throughout southern Israel.
The two Palestinians who were killed and the one apprehended in Israel were unarmed, the army admitted.
They claimed the group might have been planning to carry out resistance attacks in Israel.
Israel regularly razes civilian
homes in the occupied territories
Palestinian security sources confirmed that two men had been killed in the security zone east of Bait Hanun at around midnight.
The bodies had yet to be returned by the Israelis, the sources said, adding that they were not known to belong to any resistance group.
Meanwhile, Israeli soldiers backed by tanks and bulldozers destroyed 18 homes and partially damaged another 13 during a pre-dawn invasion into southern Gaza's Khan Yunis refugee camp, said Palestinian witnesses.
Palestinian resistance fighters detonated explosives wounding two soldiers, said occupation forces. The troops also came
under "massive" anti-tank and automatic gunfire during the raid.
Israel said its soldiers destroyed several homes it claimed were used as launching pads to fire mortars at the nearby Gush Katif Jewish settlement bloc.
There were no reported Palestinian injuries.
The Hamas resistance group, spearheading the Intifada, said it fired 26 mortar bombs at Jewish settlements in the Gaza Strip on Sunday.