Indirect talks between Israeli and Palestinian delegations are now underway in Cairo as the Israel-Hamas ceasefire enters its second day.
Israel has offered an extension of the 72-hour ceasefire.
Palestinians say their demands include the lifting of an eight-year blockade of Gaza and the opening of border crossings. The Israeli side wants Gaza to be fully demilitarized.
Egyptian mediators are now shuttling between the two delegations.
Meanwhile, UN Secretary General Ban Ki-moon has made a stern and emotional plea for the lasting peace.
"The senseless cycle of suffering in Gaza, and the West Bank, as well as in Israel, must end. Do we have to continue like this? Build, destroy and build and destroy? We will build again, but this must be the last time to rebuild; this must stop now. They must go back to the negotiating table."
The UN chief also calls for an investigation into Israel's bombing of UN facilities in Gaza.
However, Israeli Prime Minister Benjamin Netanyahu has defended the actions of Israel's military.
"I think it was justified, I think it was proportionate, and that doesn't in any way take away from the deep regret we have for the loss of a single civilian. We've gone to extraordinary lengths to avoid civilian casualties. Hamas has gone to extraordinary lengths to ensure that they have civilian casualties."
As the Egypt-brokered ceasefire holds, residents in Gaza start going outdoors.
Dozens of trucks carrying aid and supplies have entered Gaza.
Israel withdrew ground forces from the Gaza Strip on Tuesday following about a month of fighting.
