His peace push came as Israel was poised to intensify a ground operation inside the besieged Palestinian territory it says is necessary to stop militants tunnelling into the Jewish state.
Despite the pounding, Palestinian commandos succeeded in infiltrating Israel, sparking a deadly skirmish with an army patrol, as Gaza's bloodiest conflict since 2009 showed no let-up.
The United States urged its Israeli ally to do more to limit the high civilian death toll from the operation while supporting the Jewish state's right to defend itself.
President Barack Obama said Washington was "deeply concerned about the risks of further escalation and the loss of more innocent life."
He added that Washington was "hopeful" that Israel would operate "in a way that minimises civilian casualties".
But Israeli army chief Lieutenant General Benny Gantz, said the army was "expanding the ground phase of the operation."
"There will be moments of hardship," he warned in a briefing to the military, anticipating further Israeli casualties.
Troops killed a Palestinian militant who tunnelled into southern Israel but others managed to withdraw back into Gaza, an army statement said.
"Several terrorists infiltrated Israel through a tunnel from the central Gaza Strip," it said, adding that they fired a machine gun and anti-tank missile at an army patrol.
Troops "returned fire, killing a terrorist and forcing the rest back into Gaza."
Hamas's military wing, the Ezzedine al Qassam Brigades, said its fighters had carried out the raid.
"The Qassam Brigades carried out an operation behind enemy lines," it said in a statement. "Heavy fighting is ongoing with the forces of the occupation."
In a separate incident, the army said, militants had strapped explosives on to a donkey in an attempt to attack troops.
"Yesterday (Friday) evening, there was at least one such attempt, in which a donkey suspiciously began to approach forces," it said.
"The forces engaged the donkey and it exploded at a safe distance."
There have been three Israeli deaths so far since the July 8 start of the Operation Protective Edge campaign to stamp out rocket fire from Gaza.
A Bedouin was killed Friday and four of his family wounded -- including two young children -- when a rocket hit their desert campsite near Israel's Dimona nuclear reactor, police said.
Another civilian died Tuesday when a mortar round exploded in Israel and a soldier was killed by friendly fire inside Gaza on Friday.
Israel has said the aim of the ground operation launched on Thursday night is to destroy Hamas's network of tunnels which are used for cross-border attacks on southern Israel.
Military spokesperson Lieutenant General Peter Lerner told journalists Saturday that during the past 24 hours the military had seized 13 tunnels into Israel.
The UN said Ban would leave for the region Saturday to help Israelis and Palestinians "end the violence and find a way forward," under secretary general for political affairs Jeffrey Feltman told the Security Council.
Israeli Prime Minister Benjamin Netanyahu said he had ordered the military to be ready for "a significant broadening of the ground activity."
He said the ground operation was necessary to deal with the tunnels, but admitted there was "no guarantee of 100% success."
In Gaza, after a relative lull Friday, violence picked up again in the evening, with intensifying tank shelling and air strikes killing more than a dozen people.
A six-year-old child and five members of a single family, including girls aged six and two, were those killed on Saturday, emergency services spokesperson Ashraf al Qudra said.
The UN agency for Palestinian refugees UNRWA has opened 44 of its schools to shelter those fleeing homes in the most heavily bombarded areas.
It said on Saturday there were more 50,000 Gazans seeking sanctuary so far.
The World Food Programme said it had already distributed emergency food rations and food vouchers to more than 20,000 displaced people.
It said it was gearing up for a huge increase in the coming days and hoping to reach 85,000 people with food distributions.
Gaza was also struggling with a 70% power outage after electricity lines from Israel were damaged, officials said.
French Foreign Minister Laurent Fabius, who was also in Cairo to join peace efforts, called for an urgent truce.
"The absolute priority is a ceasefire, but it must guarantee a lasting truce," he said, adding that it should take into account "Israel's security" and Palestinian demands.
Hamas has rejected Egyptian proposals for a truce, demanding an easing of a harsh Gaza blockade imposed by Israel in 2006 and the release of Palestinian prisoners.
Israel pulled out of Gaza in 2005. Hamas drove out loyalists of Abbas two years later but to the dismay of Israel reconciled with the Palestinian president after US-brokered Middle East peace talks collapsed earlier this year.
COMMENTS (12)
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@prsharma, No not the whole world, there are very few of your kind. And the world will have one less fool if you educate yourself.
@p r sharma
Gaza is an open air prison, they want freedom ... them firing rockets is to get their right to freedom.
@p r sharma:
Perhaps you can educate us on who violated the ceasefire of 2012. Gaza is the world's largest open air prison and Israel has been launching airstrikes at will without any accountability.
The problem is that Israel will not stop automatically. Perhaps you need to retake a history lesson.
Three were hiking in the occupied territory and got killed by unknown criminals. Three three three have so far been reported killed in revenge which include children. Does Mr Noon know as to how many days have been allowed to Israelis to keep on killing palestinian prisoners in Gaza Prison? Genocide is the term which the Turkish Prime Minister is using, whereas the European former colonialists are singing the agreed phrase, Israel has the right to defend its citizens against the Hamas rockets.
Rex Minor
@Sami: Typical anti American blather - USA has condemned the civilian casualties more than Pakistan. USA has provided more financial and military aid to the Palestinians than Pakistan. USA supported independent Palestinian State before Pakistan. Maybe it's time for Pakistan to step up to the plate for a change?
@Sami: why Hamas do not stop rocket firing. Israel will stop automatically.. what you perceive ( genocide ) as the correct one while willfully ignore the other side. what do you think that the whole world is fool ?
@Aamir - Toronto: Stop oil to the western world and THEN you will see genocide
@JEJ.....Malala Yusofzai is a Western stooge, she can voice her concern for missing girls in Nigeria but she will never utter a single word for the innocent children who are being butchered by Zionists on daily basis.
Israel will annihilate in days if the Arab leaders wake up from deep sleep and cut off the oil supply to the Western world like the great king (Faisal bin Abdul Aziz Al Saud) of KSA did in 1973.
"The United States urged its Israeli ally to do more to limit the high civilian death toll from the operation while supporting the Jewish state’s right to defend itself". Genocide by Zionists and full backing by USA while this so called civilised world tells us about human rights. USA and its allies all are terrorist states.
Why does anyone even want to head the UN? The most impotent position in the world!
I do hope Islamic icons and peace activists like Malala Yusofzai would come out strongly for sisters in Palestine.