An Israeli military spokeswoman confirmed soldiers opened fire on a group of Palestinians who approached the fence.
An Israeli aircraft also attacked a two-story house belonging to a Hamas member in the northern Gaza Strip on Thursday, killing at least two Palestinians and wounding at least 20 others, Hamas and medical workers said.
There was no immediate Israeli comment on the incident in which Hamas said several women and children were among the wounded.
Hamas said the air strike targeted a house belonging to Ahmed Hamouda, a local commander of its armed wing, in the town of Beit Lahiya.
It was not clear whether Hamouda was inside the house at the time of the blast.
Israeli forces also attacked a group of Hamas fighters near Jabaliya, in northern Gaza, witnesses said.
It was not immediately clear whether there were casualties.
Chance to truce
The fighting came one day after the Israeli government decided to pursue Egyptian-mediated efforts to reach a truce in and around Gaza, while at the same time ordering the armed forces to prepare for an offensive in case the negotiations fail.
Israel's point man in the cease-fire talks, Amos Gilad, was traveling to Egypt to help clinch a deal.
Israeli government and security officials said Israel is willing to give the Egyptian mediation efforts about two more weeks to succeed, but if those efforts fail, it will launch its Gaza invasion.
Major points of contention remain, most prominently, Israel's demand to link the truce deal to the release of an Israeli soldier held captive by Hamas for two years, and Hamas' demand that Israel open Gaza's border crossings.
The closure has prevented the vast majority of Gaza's 1.4 million people from traveling abroad, and led to widespread shortages of fuel, electricity and basic goods.
At least 500 people, nearly all Palestinians, have been killed since peace talks between Israel and the Palestinian leadership resumed last November, according to an AFP count.