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.
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.