"Abed, 32, a resident of Kafr Dan, was a member of Hamas's terror infrastructure in the village, an infrastructure that attempted to dispatch a suicide bomber into Israel," it said.
"After the failed attempt, cell members were arrested by Palestinian security forces. Despite this, the group continued to be involved in terror, and had been planning an imminent terror attack."
Speaking about the second shooting, an Israeli army spokesman told the AFP news agency: "At around 3 o'clock an army force identified a suspicious person crossing the fence from Gaza into Israel near Kissufim.
"The force called on him to stop and fired warning shots but he did not stop and the soldiers fired at him and killed him. When they approached his body they saw he was unarmed."
Muawiya Hassanin, the head of Gaza emergency services, confirmed that a Palestinian was shot and killed in the Kissufim area.