Watch: Hamas fires dozens of rockets over Israel
The truce proposal, which Cairo laid out early on Tuesday (NZT) won US support, but Hamas, whose militants have fired more than 1000 rockets into Israel, ruled out any end to the fighting without a full agreement.
One Hamas leader said the movement had not yet formulated an official position on the proposal, but rockets continued to be fired after the deadline.
By 1200 GMT (midnight Tuesday NZT) Israel had announced it was resuming its operation.
Tensions were also high on Israel's other borders.
Overnight, three rockets hit in and around the southern resort city of Eilat wedged between Jordan and Egypt. Another fired from Lebanon struck just outside the northern coastal town of Nahariya, the army said.
A rocket fired from the Syrian Golan Heights also struck the Israeli-occupied sector of the strategic plateau, prompting the air force to launch a pre-dawn strike, killing four people, the Syrian Observatory for Human Rights said.
Watch more: Israel, Gaza exchange rocket fire
As the violence resumed, Israeli Prime Minister Benjamin Netanyahu warned Hamas that the Jewish state would not hesitate to resume its punishing campaign in and around Gaza.
"We responded positively to the Egyptian proposal to give a chance to deal with the demilitarisation of Gaza," Netanyahu said, referring to Hamas's arsenal of missiles and rockets.
"But if Hamas doesn't accept the ceasefire proposal - and that's how it seems at this point in time - Israel will have all the international legitimacy to broaden its military activity in order to achieve the necessary quiet."
Cairo's initiative was made after Washington warned Israel against a launching a ground offensive in Gaza, where troops and armour have massed along the border.
Palestinian children look through a damaged wall following an Israeli missile strike. Photo / AP
Israel launched Operation Protective Edge before dawn on July 8, hitting Gaza with an intensive air and artillery bombardment aimed at stamping out rocket fire. Militants answered with over 1000 rockets, dozens of which have targeted central and even northern Israel.
So far, the conflict has claimed 193 Palestinian lives, with human rights groups saying well over two-thirds are civilians.
There have been no deaths in Israel, although four people have been seriously wounded.
Iron Dome safety comes at a hefty cost
On the outskirts of the Israeli city of Ashkelon, two state-of-the-art anti-missile defence batteries stand on high alert.
Shaped like two giant match boxes tilted diagonally towards Gaza, the system comes to life as the wailing of a siren echoes through the nearby loudspeakers.
In the time that it took to read the two sentences above, the Iron Dome system will have determined whether the rocket soaring through the sky is likely to land in an open field or crash into a building in a city.
An Iron Dome system fires to intercept a rocket from Gaza in the Israeli city of Ashkelon. Photo / AP
In the case of the latter, a counter-missile will already have been deployed to intercept it.
More than 800 rockets have been launched at Israel from Gaza in the past week. Of these, the Iron Dome has intercepted at least 130.
The system, designed and built by Rafael Advanced Defence Systems in 2011, is configured to only destroy the rockets poised to hit urban or strategically sensitive areas.
Each interception missile fired is priced at US$50,000 (NZ$56,734). In the war with Gaza in November 2012, the Iron Dome blocked almost 500 rockets - a total cost of US$25 million.
There are seven Iron Dome batteries deployed around Israel, and so far they have had an almost 90 per cent interception success rate.
The Iron Dome is susceptible to occasional failures. In the 2012 war, an error resulted in a rocket crashing through the walls of a house in Kiryat Malachi, southern Israel, killing three people. Rafael said the system has since undergone significant improvements.
How the Iron Dome works
1 Its radar detects a rocket, sends information about it to the Iron Dome battery control centre
2 The centre works out if the rocket will hit populated areas
3 If the rocket is a danger, one of 20 missiles is fired from the launcher
4 The missile is guided by the control centre and its radar
5 The missile destroys the rocket by exploding near it
- AFP, AAP, Independent, Telegraph Group Ltd, AP