Cairo, Egypt (BBN)-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, reports BBC.
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.
US Secretary of State John Kerry has urged both sides to use the ceasefire to move towards broader negotiations.
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.
Hundreds of thousands of displaced Palestinians in Gaza have been returning to their homes. Many have found nothing left.
We met the Za'Noun family in Beit Hanoun, one of the worst affected areas right on the border with Israel. Their family home has been destroyed for the third time.
The Za'Nouns will rebuild again. "Where else can we go?" Khalil Za'Noun, 80, asked me.
One of his 34 grandchildren, Mohammed, has already lived through four wars in his short life. He's just 14.
But this will not be the last war in Gaza. This truce is only a short-term fix. None of the big issues between Israelis and Palestinians has been fixed.
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.
John Kerry told the BBC that the US fully supported Israel's right to defend itself against militant rocket attacks.
"No country can live with that condition, and the United States stands squarely behind Israel's right to defend itself in those circumstances. Period."
US Secretary of State John Kerry, speaking to BBC Hardtalk: "There has to be a giving on both sides"
Asked whether he supported Palestinian demands for a lifting of Israel's blockade of Gaza, Kerry said: "What we want to do is support the Palestinians in their desire to improve their lives and to get food in and to open crossings and to reconstruct and have greater freedom."
Kerry said a "bigger, broader approach to the underlying solution of two states" was needed - one that would provide security for Israel and "a better life and greater freedoms for the Palestinians".
The 72-hour truce came into effect at 08:00 local time (05:00 GMT) on Tuesday.
Israel withdrew all forces to positions outside Gaza - and many Gazans began to return.
Carpenter Mahmoud Al Maghani, 44, found that his property in the Shejaiya neighbourhood, east of Gaza City, had been completely destroyed.
"I think my workshop was here, but honestly I can't make sure of that," he told the Associated Press. "I came yesterday and all I found was rubble."
Some Israelis close to the border were unconvinced the military had finished its job removing tunnels used by militants to infiltrate Israel.
"Who can promise me that all the tunnels have been destroyed? I am angry that they are not pressing on with the offensive," Leah Musafi, who lives on the Nir Am kibbutz, told Reuters.
Israel launched Operation Protective Edge on 8 July with the stated aim of ending rocket attacks and destroying tunnels used by Palestinian militants.
The latest figures from Gaza's health ministry list 1,867 deaths. Some 63 Israeli soldiers and four civilians in Israel have died.
Gaza's Deputy Economy Minister Taysir Amro said the cost could be up to $6bn (£3.55bn).
Separately, Israel has revealed it has arrested a Palestinian suspected of involvement in the kidnapping and murder of three Israeli teenagers in June. Hussam Qawasmeh was arrested on 11 July.
The deaths and subsequent apparent revenge killing of a Palestinian teenager were key factors in escalating tension.
BBN/SS-06Aug14-5:30pm (BST)