This is the first time since the early hours of Sunday morning that the Egypt-brokered cease-fire between Israel and Gaza terror groups has been broken. The Democratic Front for the Liberation of Palestine said the men were members of their organization.
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During Sunday's weekly cabinet meeting, Prime Minister Benjamin Netanyahu said, "There is no cease-fire and the other side will pay a heavier price than it has so far, until it ceases fire." The prime minister also praised Israel's southern residents for their standing.
Eleven rockets and mortar shells were fired at southern Israel overnight and early Sunday morning before the cease-fire came into effect.
Earlier, an Islamic Jihad leader said that the organization was committed to the ceasefire that has been brokered by Egypt after a day of violence saw nine Palestinian operatives and an Israeli civilian killed.
"When all jet fighters leave the skies of Gaza we will stop firing rockets," said Dawud Shehab of Islamic Jihad.
Defense officials said Israel was also holding back in an effort to keep the violence from escalating further.
Prime Minister Benjamin Netanyahu said that Israel's policy in the Gaza Strip included two main principles: "Kill or be killed" and "Hurt us – on your own head be it".
Netanyahu stressed that while Israel does not seek to deteriorate the security situation, "we will defend ourselves according to these principles."
Elior Levy and AP contributed to the report