"Israel has accepted Egypt's proposal," a senior Israeli government official said, adding Israeli negotiators would return to Cairo today to resume indirect talks with the Palestinians if the truce held.
The Israeli team had flown home on Friday before a previous three-day truce expired and hostilities in the month-old conflict broke out again.
A Hamas official said Palestinian factions had accepted Egypt's call and that the Cairo talks would continue.
In a statement, Egypt's Foreign Ministry urged "both sides to exploit this truce to resume indirect negotiations immediately and work towards a comprehensive and lasting ceasefire agreement".
Earlier, Israeli Prime Minister Benjamin Netanyahu said "Israel will not negotiate under fire" and warned of a protracted Israeli military campaign in the Gaza Strip if rocket salvoes continued.
Hamas has demanded an end to Israeli and Egyptian blockades of the coastal territory and the opening of a Gaza seaport - a project Israel says should be dealt with only in any future talks on a permanent peace deal with the Palestinians.
Israeli air strikes and shelling yesterday killed five Palestinians in Gaza, including a boy of 14 and a woman, medics said, in a third day of renewed fighting. Since the previous ceasefire expired, Palestinian rocket and mortar salvoes have focused on Israeli kibbutzim, or collective farms, just across the border in what appeared to be a strategy of sapping the Jewish state's morale without triggering another ground invasion of the tiny Gaza Strip.
A month of war has killed 1895 Palestinians and 67 Israelis while devastating wide tracts of densely populated Gaza. But international pressure for a ceasefire has been weaker than in earlier rounds of Israeli-Palestinian conflict, given other international security crises, notably in Iraq and Ukraine, distracting major powers.
However, the violence over the past three days has been less intense than at the war's outset, with reduced firing on both sides. Israel withdrew ground forces from Gaza on Tuesday.
Before the truce ran out, Israel said it was ready to agree to an extension. Hamas did not agree, calling for an end to the economically stifling blockade of the enclave that both Israel and Egypt, which regards the Islamist movement as a security threat, have imposed.
Israel has resisted easing access to Gaza, suspecting Hamas could then restock with weapons from abroad.
A sticking point has been Israel's demand for guarantees that Hamas would not use any reconstruction supplies sent to Gaza to build more tunnels of the sort that Palestinian fighters have used to infiltrate the Jewish state.
Egypt is meeting separately with each party, given that Hamas rejects Israel's right to exist and Israel regards the group as a terrorist organisation.
Gaza hospital officials say the Palestinian death toll has been mainly civilian since the July 8 launch of Israel's military campaign to quell Gaza rocket fire.
Israel has lost 64 soldiers and three civilians to the war, where losses of non-combatants in Gaza and the destruction of thousands of homes have drawn international condemnation.
Israeli tanks and infantry left the enclave on Tuesday after the army said it had completed its main mission of destroying more than 30 tunnels dug by militants for cross-border attacks.
In renewed fighting since the end of a three-day truce on Friday, Israel has killed 16 Palestinians in air strikes.