Medical sources said Ahmed al-Bureim, 18, and Abu Lahia, 27, a member of the Palestinian national security force, were killed earlier in the day, not far from Abassan.
The Israeli army confirmed its forces were operating in southern Gaza as part of an ongoing offensive launched after the abduction of a soldier in a cross-border raid near Gaza on June 25.
In Beit Hanun, in the north, 37-year-old farmer Suheil al-Majdalawi was fatally shot by Israeli soldiers while in his fields, a medical source said.
The army said its forces identified three people "acting in a suspicious way 100m from the security fence" near Beit Hanun.
Exchanges of fire
In other violence, an Israeli reserve soldier was wounded in exchanges of fire with Palestinians early Thursday, an army spokeswoman said.
And in the occupied West Bank, an Israeli was lightly wounded when his car was shot at near the Jewish settlement of Telem, some 8km west of the southern city of Hebron, a military source said.
No other details of the incident were immediately available.