Hassen Chalghoumi, from Tunisia, pioneered a religious exchange in France.
Israel and the US don't want rebuilding homes to become rebuilding Hamas.
Two key issues are Israel's demand to stop arms smuggling and the Palestinian desire for an end to the economic blockade of Gaza.
Israel seeks US help on Gaza weapons smuggling, while Arab nations remain divided over a truce.
The UN headquarters in Gaza was struck by Israeli fire. Fissures are emerging among Israeli civilian and military leaders over how and when to end the campaign.