Palestinian factions were to meet in Egypt next week to further discuss the Hamas plan.
Food aid suspension
The proposal came as the UN suspended aid deliveries to more than half a million people in Gaza after its delivery lorries ran out of fuel.
The United Nations Works and Relief Agency (UNRWA), which distributes food and essential commodities to nearly two-thirds of Gaza's population, had earlier warned it expected to run out of fuel by Thursday afternoon.
The last shipment of fuel to Gaza by Israel - the sole distributor of it to the territory - came before Palestinian fighters attacked an Israeli fuel depot on April 9.
An emergency shipment of fuel for UNRWA lorries from within Gaza was reportedly intercepted on Thursday by angry strawberry farmers who needed the supplies for irrigation and refrigeration.
"It's something that we've been warning about since early April, and that is what is so tragic," John Ging, head of UNRWA in the Gaza Strip, told Al Jazeera.
"Now we're at a standstill - we just don't have the fuel to operate the trucks.
"We have the food, and we certainly have hundreds of thousands of desperate people who need it. But this is the situation tonight."
Israel has besieged Gaza since fighters from Hamas's armed wing routed Palestinian Authority forces loyal to rival Fatah there in June.