As the violence raged for a sixth day, an Israeli missile killed a senior Islamic Jihad militant in a Gaza City tower housing Palestinian and international media, the second time in as many days the building has been targeted.
As Ban arrived in Cairo to push for a ceasefire, Hamas chief Khaled Meshaal said his movement was committed to efforts to secure a truce with Israel, but insisted the Jewish state must lift its six-year blockade of the Gaza Strip.
Terrified and desperate, many Gaza families have fled their homes, some seeking haven in the south which has seen fewer strikes. But they know nowhere is safe.
"My son Mohammed refuses to eat. He follows me everywhere because he's so scared and asks me every 10 minutes when we're going to die," said Umm Jihad, 37.
"He says he won't go back to school because he's scared he'll be martyred or that he'll come back from school and find that I or his brothers have been killed," she told AFP.
Mourners flocked to the funeral of nine members of one family killed in a weekend strike on a Gaza City home, the tiny bodies of the five children carried through the streets wrapped in Palestinian flags.
"Do children fire rockets?" shouted a man through a loudspeaker, as the crowd roared back: "No!"
The violence, which comes as Israel gears up for a general election on January 22, raised the spectre of a broader Israeli military campaign like its 22-day Operation Cast Lead, launched at the end of December 2008.
Analysts say Israel's leadership appears satisfied with the success of Operation Pillar of Defence and that could it be ready for a ceasefire.
But the Jewish state has signalled it is ready to expand the operation.
And Gaza's Hamas rulers have been emboldened after securing the support of the recently installed Islamist governments of Egypt and Tunisia.
-- Death toll mounts --
The overall death toll from the Israeli raids on the Palestinian territory hit 101, with another 24 people killed on Monday.
The Israeli army said that 42 rockets had struck on Monday and another 19 been intercepted by the Iron Dome defence system.
To date, the Israeli military has struck more than 1,350 targets in Gaza, and 640 rockets have crashed into southern Israel while another 324 have been intercepted.
The latest negotiations aimed at ending the conflict, conducted behind closed doors in Cairo, ended without agreement. But all sides have expressed a willingness to engage in more talks.
"We are committed to a ceasefire, but Israel must stop its aggression," Meshaal told a Cairo news conference.
Israel was also seeking a ceasefire, with Prime Minister Benjamin Netanyahu himself having "called the US, Europe and Egypt asking for a truce," said Meshaal.
"We are not against a calming, but we want our demands... to end the thuggery, to end the aggression and to lift the blockade," he said.
An Egyptian official who spoke to AFP before Meshaal's statement reported "encouraging signs".
"I hope, that maybe by the end of the day, we receive a final signal of what may be achieved to stop hostilities," he said.
"Both sides are saying a ceasefire is important and that there should be guarantees, but these guarantees are different."
Hamas is also understood to be seeking guarantees Israel will stop its targeted killings, like the one which killed a top military commander on Wednesday, sparking the current round of hostilities.
Israel has its own demands, with Foreign Minister Avigdor Lieberman insisting "the first and absolute condition for a truce is stopping all fire from Gaza."
Turkish Foreign Minister Ahmet Davutoglu is to join a delegation led by Arab League chief Nabil al-Arabi on a solidarity mission to Gaza on Tuesday, the latest in a series of visits that have eased the long diplomatic isolation of the territory's Hamas rulers.
A string of international diplomats have visited the region in recent days in a bid to end the bloodshed. Middle East peace Quartet envoy Tony Blair is in Jerusalem and German Foreign Minister Guido Westerwelle was to arrive later on Monday.