Israel and Hamas said on Thursday that Egypt was mediating a restoration of a 2014 truce after two days of cross-border violence that wounded four Palestinians, among them three children.
The woundings occurred in Zeitoun during air strikes early on Thursday that targeted Hamas training camps.
Hamas political leader Mousa Abu Mazouk wrote on his Facebook page on that Egypt had helped to restore calm along the tense frontier.
Abu Marzouk, the deputy head of Hamas' political bureau, said Hamas had contacted Egypt, mediator of the 2014 truce, and the Egyptians responded "immediately and seriously and acted to restore the situation to the status quo ante."
The IDF also confirmed that the Egyptians were mediating to achieve a restoration of calm between Israel and Hamas.
The air force had struck at four Hamas targets in response to shootings at Israeli soldiers operating near the border on Wednesday, the IDF said.
"The IDF sees terrorist activities conducted above or below the ground as a violation of Israel's sovereignty, and sees the Hamas terrorist organization as solely responsible for this terrorist activity," the IDF statement said.
"Quiet and regular daily routine are a mutual interest and we will strive to keep them," it added.
In his Facebook post, Abu Mazouk blamed the two days of violence on an Israeli attempt to set new facts on the ground 150 meters inside Gaza which he said "compelled resistance forces to intervene."
Israel said it was responding to mortars shot by Hamas. The IDF accused Hamas of firing "more than five mortar rounds at forces during operational activities adjacent to the security fence with the Gaza Strip.".
Defense sources said on Wednesday they believed Hamas's shootings were aimed at trying to deter Israeli forces from searching for tunnels.
Reports in Rafah, in the southern Gaza Strip, said five airstrikes early on Thursday targeted Hamas training camps near the airport and in the center of the enclave.
During Wednesday's violence, the IDF declared the border area a closed military zone, barring access between the Saad Junction to Kibbutz Nahal Oz to anyone but residents.
During Wednesday's incidents, a mortar shell was fired from Gaza toward the northern part of the border fence, where Israeli forces are present, near Nahal Oz. Israeli tanks returned fire toward two Hamas positions in Shujaiya.
After the tanks fire, Hamas ordered two neighborhood schools in Shujaiya evacuated, as a precaution due to Israeli shooting. Evening classes were cancelled.
Hamas' Interior Ministry also said it was evacuating security centers in the Strip for fear of Israeli attacks.
Islamic Jihad published a statement warning of the repercussions of an Israeli escalation.
The Palestinian information center run by Hamas reported that "resistance forces" fired mortars and a 107 mm rocket at Nahal Oz after the "Israeli escalation."
The cross-border shootings began on Tuesday afternoon when light arms fire was directed at the IDF operating near northern Gaza. There were no casualties, but two pieces of heavy machinery were damaged.
Despite its mortar attacks, Hamas signalled it wasn't seeking an escalation and blamed the violence on Israel.
A Hamas political activist told Haaretz from Gaza "Hamas has no intention of breaking the rules of the game and believes that Israel is also not interested in an escalation.
"What has been going on in recent hours is a type of dialogue via mortars and artillery fire," he said. "Israel is shooting in a measured way and Hamas is also permitting mortar fire. In Gaza there is no atmosphere of escalation on the horizon or any change in the conduct of its civilians."
The violence was seen as unusual, with the IDF saying Hamas had not fired "a single bullet" at Israel since the truce that ended two month long Operation Protective Edge in 2014.
A senior officer in the IDF's Southern Command said on Wednesday that Hamas had created a force to police the border region, preventing terrorist attacks and rocket fire at Israel.
That being said, the Hamas has also been digging tunnels into Israeli territory and developing weapons such as rockets and drones.
A recently revealed tunnel stretching from Gaza into Israel, which the IDF has destroyed was meant as a staging ground for an attack, the Israeli military has said. It was dug before the last war took place though Hamas had more recently been working on it, the IDF said.
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