Israel has agreed to extend a ceasefire that ended a month of fighting in Gaza beyond a Friday deadline, an Israeli official said on Wednesday, speaking on condition of anonymity.

"Israel accepted an unconditional 72-hour cease fire, and is willing to extend an unconditional cease-fire," the official said.

The official did not say for how much longer Israel had agreed to extend the truce, only that: "Israel has expressed its readiness to extend the truce under its current terms," referring to the deal brokered by Egypt that took effect on Tuesday.

Cairo-based  senior Hamas official Musa Abu Marzouk said in a Twitter post Wednesday night that "there is no agreement on an extension" of the Gaza truce.

A senior official with the Islamist group's armed wing threatened earlier to quit the talks without progress towards achieving its demands to lift a Gaza blockade and free prisoners held by Israel.

Hamas also warned Wednesday night that it would resume its attacks on Israel unless Jerusalem accepts all Palestinian demands, first and foremost the lifting of the siege and release of prisoners who were rearrested in the West Bank.

Hamas official Izzat al-Risheq said, "We haven't received a reply to our demands. Our fingers are still on the trigger."

Chief of Staff Lieutenant-General Benny Gantz, has said in televised remarks that should Hamas disrupt the calm, "we will not hesitate to continue to use our force wherever necessary and with whatever force necessary to ensure the security of Israeli citizens near and far."

Israel withdrew ground forces from tiny, densely populated Gaza on Tuesday morning and started a 72-hour, Egyptian-brokered ceasefire with Hamas as a first step towards a long-term deal.

It showed signs of expecting the truce to last by lifting official emergency restrictions on civilians living in Israel's south near Gaza, permitting more public activities and urging everyone to resume their routines.

Streets in towns in southern Israel, which had been under daily rocket fire from the Gaza Strip, were filled again with playing children. The military said that two rocket-warning sirens sounded in the south proved to be false alarms.

US envoy Frank Lowenstein was due in Cairo on Wednesday night to try to help Egyptian-mediated talks between Israel and the Palestinians find a lasting end to their conflict over the Gaza Strip, the US State Department said.

Lowenstein is the acting US special envoy for Israeli-Palestinian negotiations.

"We, along with our partners, are working to find a way forward that brings an end to the violence and addresses the underlying causes of this crisis," State Department spokesman Edgar Vasquez said in announcing the trip.

Herb Keinon  and Khaled Abu Toameh contributed to this report.

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