An Israeli official said the Israeli delegation, which left Cairo on Friday morning, would return on Monday if the cease-fire held overnight but warned that Israel would not negotiate under fire.

The Egyptian Foreign Ministry said in a statement that the new lull was intended to facilitate the flow of humanitarian aid into Gaza and the repair of essential infrastructure, and to allow a window for the resumption of “indirect, immediate and continuous negotiations” for a lasting cease-fire.

But members of the Palestinian delegation expressed frustration earlier Sunday over what they said was an emphasis by the Egyptian mediators and the Israelis on winning a cease-fire at the expense of longer-term solutions that would end the isolation of Gaza. One of Hamas’s central demands is a complete lifting of the blockade of Gaza and the free movement of people and goods through its border crossings with Israel and Egypt. Hamas has also demanded the construction of a seaport and the reconstruction of Gaza’s airport.

Israel, for its part, wants to see Hamas come out of the negotiation process weakened and without any obvious rewards.

“The day after should be based, on the one hand, on providing for the economic and social needs of the people of Gaza, without strengthening Hamas,” said Tzipi Livni, a moderate Israeli minister who has pushed for a permanent peace deal with the West Bank Palestinian leadership. But, speaking to reporters in Jerusalem on Sunday, Ms. Livni said any Gaza solution should also be based on Israel’s security concerns, and she called for a mechanism to prevent Hamas from rearming, which is now also an Egyptian interest, and the eventual demilitarization of Gaza.