A Gaza ceasefire was holding on Wednesday and U.S. Secretary of State John Kerry, echoing Israel's position, linked a lifting of blockades of the devastated enclave to Hamas giving up its rocket arsenal.
Israel withdrew ground forces from the Gaza Strip on Tuesday morning and started a 72-hour ceasefire with Hamas mediated by Egypt as a first step towards negotiations on a more enduring end to the month-old war.
"What we want to do is support the Palestinians and their desire to improve their lives and to be able to open crossings and get food in and reconstruct and have greater freedom," Kerry said.
"But that has to come with a greater responsibility towards Israel, which means giving up rockets, moving into a different plane," he said on the BBC's HARDtalk program.
Kerry said all this would "finally come together" as part of wider Israeli-Palestinian peace efforts that he has spearheaded but which have been frozen since April over Israel's opposition to a unity deal between Hamas and Western-backed President Mahmoud Abbas's Palestine Liberation Organization.
Israel sent officials to join talks in Cairo to cement a longer-term deal during the course of the current truce. Hamas and Islamic Jihad also dispatched representatives from Gaza.
In Gaza, where some half-million people have been displaced by a month of bloodshed, some residents left U.N. shelters to trek back to neighborhoods where whole blocks have been destroyed by Israeli shelling and the smell of decomposing bodies fills the air.
Israeli Prime Minister Benjamin Netanyahu's security cabinet met late on Tuesday to discuss the aftermath of the fighting and strategy for the Cairo negotiations.