The quartet's envoy to the Middle East, Tony Blair, told Israeli President Shimon Peres on Monday it is trying to end the fighting between Israel and Gaza- based militant groups.

According to Blair, who represents the UN, the United States, Russia and the EU, the quartet is working together with Egypt to bring to a cessation of the fighting, as Operation Pillar of Defense entered its sixth day.

"While Israelis are suffering, Gazans are also suffering and we must end this situation," Blair said, following the two men's meeting at the President's chambers on Monday morning.

Blair also said that the cease-fire agreement should also include a more permanent solution to the Israeli-Palestinian conflict, not just to the current conflict with Gaza.

"What we need is a constructive approach to peace that is lasting and durable," he added.

President Peres, on his behalf, thanked Blair for the efforts the quartet is making in order to reach a lull with Palestinian militant groups in Gaza, and specifically praised Egyptian President Mohammed Morsi, who he said had a very positive role in the talks between both parties.

"The firing has to be stopped," Peres said on Monday. "Israel has no ambitions to conquer land, we just want to stop the firing of rockets from the Gaza Strip and prevent the renewal of rocket attacks," he added.

The sixth day of Operation Pillar of Defense began with a relative calm on the Israeli side after a night of attacks in the Gaza Strip.

According to Israeli Defense Forces (IDF) spokesperson, 80 targets were struck and 14 Palestinians were killed in last night' s attack, including a family of civilians.

About two dozen rockets were launched from the Gaza Strip on Monday morning towards the southern communities in Israel. No injuries were reported, but damages were caused to a school in the city of Ashkelon which was empty since no school was open in those communities.

So far out of 540 rockets launched towards Israel up until this morning, 310 were intercepted by the Iron Dome anti-missile batteries.

According to Palestinian reports, the dead count has gone up to 95 people with more than 400 people injured amid recurring air strikes by the Israeli Air Force (IAF).

The IAF struck down more than 1,000 targets in the past week in the Gaza Strip, mainly targeting chief Hamas militants, long-range missile caches, launch pads and smuggling tunnels and the Hamas headquarters, as well as media compounds.

There have been mixed reports over the past few days about whether a cease-fire is nearing or will the operation be expanded into a ground invasion to the Gaza Strip.

However, on the other hand, the international community is making great efforts over the past two days to reach a lull agreement between Israel and the militant groups.