US Secretary of State John Kerry has proposed a cease-fire plan to Israel and Hamas, which will be discussed on Friday by both sides.
Prime Minister Binyamin Netanyahu convened his security cabinet on Friday to discuss a limited humanitarian truce under which Palestinian movement would be freed up to allow in aid and for casualties to be recovered.
An Israeli official said the Netanyahu government envisages the initial halt to the fighting lasting seven days, during which the army would keep digging up tunnels on Gaza's eastern frontier.
"First Israel wants to hear Hamas's response to the (Kerry) proposals," an official said, adding that some members of the security cabinet also sought assurances that Gaza would be stripped of its remaining rockets under any extended ceasefire.
Hamas had no immediate comment on the proposal. On Wednesday, its leader Khaled Meshaal voiced support for a humanitarian truce, but only if Israel eased restrictions on Gaza's 1.8 million people.
Hamas wants Egypt to open up its border with Gaza, too, and has demanded that Israel release hundreds of prisoners rounded up by Israel in a sweep of the West Bank last month following the kidnap and killing of three Jewish teenagers.
Such concessions appear unlikely, however, as both Israel and Egypt consider Hamas a security threat.
One Cairo official said next week's Eid al-Fitr festival, which concludes Ramadan, was a possible date for a truce. But US officials were circumspect on progress made by Kerry in the mediation that has involved Egypt, Turkey, Qatar and Abbas.
"Gaps remain between the parties, so his focus is on finding a formula that both sides can accept," a senior US official said on Thursday, adding that Kerry would not stay "for an indefinite amount of time".
On Wednesday and Thursday, Kerry was in Israel after holding talks in Cairo on the situation.
He met separately with Palestinian Authority President Mahmoud Abbas and Netanyahu during his diplomatic visit.