"Israel will continue to act to protect its citizens," he told the Reuters news agency.West Bank extension
Mahmoud al-Zahar, the former Palestinian foreign minister, told reporters in Cairo on Thursday, said: "The movement agrees to a truce in the Gaza Strip ... fixed at six months, during which period Egypt will work to extend the truce to the West Bank."
He said other Palestinian factions, including Islamic Jihad and groups based in Damascus, had preliminarily approved the offer.
Al Jazeera's David Chater in Gaza said that the Egyptian mediators were due to officially present the ceasefire proposal to Israeli official next week.
"At the moment this does seem to be a very discouraging shot across Hamas's bows by Israel," he said.
"But there is no doubt that the Hamas Gaza-first proposal is a significant development and a breakthrough in terms of the fact they are willing to accept Gaza only for the the first few months of a ceasefire and then discuss ... developing it and extending it to the occupied West Bank."
However, an official close to Ehud Barak, Israel's defence minister, suggested that the two sides could still decide to hold their fire without a formal accord being agreed.
"We don't rule out a tacit agreement, on condition it is done in stages. In a first stage we demand all groups stop firing rockets. Israel would then be willing to reduce its operations if the calm continues," he told the AFP news agency.
Mahmoud Abbas, the Palestinian president, has voiced cautious support for the truce initiative.
"We hope that this proposal is a serious one, and we hope it will be taken seriously by Israel," Nimer Hammad, an aide to Abbas, said.
Israel has besieged Gaza since fighters from Hamas's armed wing routed Palestinian Authority forces loyal to rival Fatah there in June.
Food aid suspension
Meanwhile, thousands of Gazans gathered at the Rafah and Erez crossings to protest against the Israeli blockade, which on Thursday forced the United Nations Works and Relief Agency (UNRWA) to suspend aid deliveries after lorries ran out of fuel.
David Chater said that the rallies were "part of a continuing campaign by Hamas to show the plight of the Palestinian people and the corrosive effect of the siege on society".
The last shipment of fuel to Gaza by Israel - the sole distributor of it to the territory - came before Palestinian fighters attacked an Israeli fuel depot on April 9.
An emergency shipment of fuel for UNRWA lorries from within Gaza was reportedly intercepted on Thursday by angry strawberry farmers who needed the supplies for irrigation and refrigeration.
"The big picture is there is a peace process going on and this is extremely unhelpful," Chris Gunness, a spokesman for the UNRWA, said.
"Hungry, angry people do not serve the interests of peace, neither do they serve Israel's security interests."
Israel has accused Hamas of stage-managing the crisis to encourage international condemnation of Israel.
"Unfortunately, we are witnessing once again Hamas attempts to create a crisis situation in the Gaza Strip, on the back of the civilian population," Colonel Nir Press, head of the Israeli office for liaison with Gaza, said.
Also on Friday, Israeli security forces were hunting for Palestinian fighters after two security guards were shot dead at an industrial complex near the West Bank.