“As of now we have struck more than 1000 targets, so Hamas should do the math over whether it is worth or not to cease fire,” said Israeli Vice Prime Minister Moshe Yaalon.
“If there is quiet in the south and no rockets and missiles are fired at Israel's citizens, nor terrorist attacks engineered from the Gaza Strip, we will not attack,” he wrote on Twitter.
Fifty Palestinians, about half of them civilians, including 14 children, have been killed since the Israeli offensive began, Palestinian officials said. More than 500 rockets fired from Gaza have hit Israel, killing three civilians.
Israel unleashed intensive air strikes on Wednesday, killing the military commander of the Hamas Islamist group that governs Gaza and spurns peace with the Jewish state.
Israel's declared goal is to deplete Gaza arsenals and press Hamas into stopping cross-border rocket fire that has plagued Israeli border towns for years and which has now targeted Tel Aviv and Jerusalem.
Air raids continued past midnight into Sunday, with warships shelling from the sea. Two Gaza City media buildings were hit, witnesses said, wounding six journalists and damaging facilities belonging to Hamas's Al-Aqsa TV as well as Britain's Sky News.
An employee of Beirut-based al Quds television station lost his leg in the attack, medics said.
An Israeli military spokeswoman said the strike had targeted a rooftop “transmission antenna used by Hamas to carry out terror activity”. International media organisations demanded further clarification.
Three other attacks killed three children and wounded 14 other people, medical officials said.
Egyptian President Mohamed Mursi said in Cairo, as his security deputies sought to broker a truce with Hamas leaders, that “there are some indications that there is a possibility of a ceasefire soon, but we do not yet have firm guarantees”.
Egypt has mediated previous ceasefire deals between Israel and Hamas, the latest of which unravelled with recent violence.
A Palestinian official told Reuters the truce discussions would continue in Cairo on Sunday, saying “there is hope”, but that it was too early to say whether the efforts would succeed.
At a Gaza news conference, Hamas military spokesman Abu Ubaida voiced defiance, saying: “This round of confrontation will not be the last against the Zionist enemy and it is only the beginning.”
Israel's military also saw action along the northern frontier, firing into Syria on Saturday in what it said was a response to shooting aimed at its troops in the occupied Golan Heights. Israel's chief military spokesman, citing Arab media, said it appeared Syrian soldiers were killed in the incident.
There were no reported casualties on the Israeli side from the shootings, the third case this month of violence seen as a spillover of battles between Syrian President Bashar al-Assad's forces and rebels.
With Israeli tanks and artillery poised along the Gaza frontier for a possible ground operation, Prime Minister Benjamin Netanyahu convened his cabinet in Jerusalem on Sunday for its weekly meeting.
On Friday, ministers decided to double the current reserve troop quota set for the Gaza offensive to 75 000 and 30 000 soldiers have already been called up.
Israel's operation so far has drawn Western support for what US and European leaders have called its right to self-defence, but there was also a growing number of calls from world leaders to seek an end to the hostilities.
British Prime Minister David Cameron “expressed concern over the risk of the conflict escalating further and the danger of further civilian casualties on both sides”, in a conversation with Netanyahu, a spokesperson for Cameron said.
London was “putting pressure on both sides to de-escalate,” the spokesman said, adding that Cameron had urged Netanyahu “to do everything possible to bring the conflict to an end.”
Ben Rhodes, a deputy national security adviser to President Barack Obama, said the United States would like to see the conflict resolved through “de-escalation” and diplomacy, but also believed Israel had the right to self-defense.
Diplomats at the United Nations said Secretary-General Ban Ki-moon was expected to visit Israel and Egypt in the coming week to push for an end to the fighting.
A possible move into the densely populated Gaza Strip and the risk of major casualties it brings would be a significant gamble for Netanyahu, favoured to win a January election.
The last Gaza war, a three-week Israeli blitz and invasion over the New Year of 2008-09, killed 1,400 Palestinians, mostly civilians. Thirteen Israelis died in the conflict.
The current conflagration has stirred the pot of a Middle East already boiling from two years of Arab revolution and a civil war in Syria that threatens to spread beyond its borders.
One major change has been the election of an Islamist government in Cairo that is allied with Hamas, potentially narrowing Israel's manoeuvring room in confronting the Palestinian group. Israel and Egypt made peace in 1979.
In attacks on Saturday, Israel destroyed the house of a Hamas commander near the Egyptian border.
Casualties there were averted however, because Israel had fired non-exploding missiles at the building beforehand from a drone, which the militant's family understood as a warning to flee, witnesses said.
Israeli aircraft also bombed Hamas government buildings in Gaza on Saturday, including the offices of Prime Minister Ismail Haniyeh and a police headquarters.
Israel's “Iron Dome” missile interceptor system has destroyed more than 200 incoming rockets from Gaza in mid-air since Wednesday, saving Israeli towns and cities from potentially significant damage.
However, one salvo fired on Sunday evaded Iron Dome and wounded - Reuters