Indirect talks between Israeli and Palestinian representatives are taking place in the Egyptian capital Cairo.
They come after a four-week conflict in Gaza that has claimed more than 1,900 lives.
Egyptian mediators are shuttling between the two delegations, relaying each side's demands.
A 72-hour truce is now in its second day in Gaza, the longest lull in fighting since the conflict began on 8 July.
UN Secretary General Ban Ki-Moon has called for an end to the "senseless cycle of suffering" in Gaza.
Speaking at the General Assembly in New York, he strongly criticised Israel for shelling UN compounds during its offensive.
He said that while there were reports of Hamas rockets being fired from near UN premises, the "mere suspicion of militant activity does not justify jeopardising the lives and safety of many thousands of innocent civilians".
US Secretary of State John Kerry has urged both sides to use the ceasefire to move towards broader negotiations.
Mr Kerry told the BBC that the situation could "concentrate people's minds" on the need to negotiate a two-state solution.
Meanwhile, hundreds of thousands of displaced Gazans have been returning to their homes.
The BBC's Jon Donnison, in Gaza City, says many people have found nothing left.
Both sides are already acting as though this ceasefire will stick - Israel is re-opening southern road and rail routes, and people in Gaza are starting to move around more freely.
Faced with the alternative of making difficult concessions, the two sides may yet conclude that the current grudging truce is the best that can be achieved for now and that it's enough.
If this latest round of fighting ends in that way, it seems certain to pave the way to another round sometime in the future.
The Palestinian delegation at the Cairo talks includes negotiators from Hamas, the militant group that controls Gaza, as well as members of Islamic Jihad and the Palestinian Authority.
The names of those representing Israel have not been given.
The main Palestinian demands include the end of Israel's blockade of the territory and the opening of border crossings. They will also want internationally funded reconstruction.
Israeli government spokesman Mark Regev said Israel's main focus for a longer-term deal would be on demilitarising Gaza to achieve a "sustained period of quiet".
But senior Hamas official Izzat Rishq told AP: "We'd take the life of anyone who tries to take the weapons of resistance."
Meanwhile Middle East peace envoy Tony Blair and UN special co-ordinator for the Middle East peace process Robert Serry are due to hold talks with Egyptian officials later on Wednesday.
And Norway is organising a donor conference to help fund Gaza's reconstruction.
(BBC)