Prime Minister Benjamin Netanyahu has said any deal on Gaza's future had to meet Israel's security needs, warning Hamas it faced "harsh strikes" if it resumed firing into the Jewish state.
With a five-day ceasefire due to expire late today, negotiators returned after consultations to Cairo to seek an end to five weeks of hostilities that have killed more than 2,000 people.
"If Hamas thinks that through continued intermittent firing it will cause us to make concessions, it is mistaken. For as long as quiet does not return, Hamas will continue to absorb very harsh strikes," Mr Netanyahu said.
There have been two days of quiet in Gaza. No rockets or missiles, no more destroyed houses, no more ambulance sirens screaming.
A three-year-old girl has been rescued from Gaza and brought to London for life-saving heart surgery.
A small team of NHS doctors and surgeons is travel to Gaza to set up facilities and establish how best to use specialists and equipment.