Gaza's Health Ministry says Israeli troops have killed three Palestinians and severely wounded a fourth near the heavily guarded perimeter fence.
The Israeli military said on Sunday that a helicopter and a tank fired at armed suspects near the fence overnight.
After weeks of calm, Palestinian militants have attempted a number of raids in recent days. They fired rockets into Israel on two occasions over the weekend, without wounding anyone.
Israel holds Hamas responsible for all attacks emanating from Gaza, which the Islamic militant group has ruled since 2007. Hamas has said recent attacks were carried out by individuals frustrated by the Israeli-Egyptian blockade imposed on the territory 12 years ago.
Israeli-Palestinian tensions have also risen following recent attacks in the occupied West Bank and clashes at a Jerusalem holy site.