As the United States and Egyptian mediators head to Israel to begin de-escalation talks, the antagonists are weighing delicate internal considerations before agreeing to discussions on ending the violence.

Both Israel and Hamas first have to find ways to spin a narrative of victory for their publics, analysts say, but the task will be easier for Hamas than for Israel.

Israel’s caretaker prime minister, Benjamin Netanyahu, has to calculate the impact of the fighting on his own political fortunes, made more complicated by the internal unrest between Jews and Israeli Arabs in numerous cities inside Israel. The crucial decision for Israel is whether “victory” requires sending ground troops into Gaza, which would extend the conflict and significantly increase the number of dead and wounded on both sides.

For the Palestinians, the indefinite postponement of elections last month by the Palestinian president, Mahmoud Abbas, created a vacuum that Hamas is more than willing to fill. Hamas argues that it is the only Palestinian faction that, with its large stockpile of improved missiles, is defending the holy places of Jerusalem, turning Mr. Abbas into a spectator.

President Biden has spoken to Mr. Netanyahu and repeated the usual formula about Israel’s right to self-defense, and he has dispatched an experienced diplomat, the deputy assistant secretary of state Hady Amr, to urge de-escalation on both sides.