Israel pounded targets across the Gaza Strip on Tuesday, saying no ceasefire was near as top US and UN diplomats pursued talks on halting fighting that has claimed more than 600 Palestians and 27 Israeli soldiers.
US Secretary of State John Kerry held discussions in neighbouring Egypt, while UN Secretary General Ban Ki-moon flew to Israel to see Prime Minister Benjamin Netanyahu and meet on Wednesday with the Palestinian prime minister in the occupied West Bank.
However, there was no let-up in the Israeli assault on Gaza, with plumes of black smoke spiralling into the sky, and Israeli shells raining down on the coastal Palestinian enclave.
"A ceasefire is not near," said Justice Minister Tzipi Livni, viewed as the most dovish member of Israeli Prime Minister Benjamin Netanyahu's inner security cabinet.
"I see no light at the end of the tunnel," she told Israel's Army Radio.
Dispatched by US President Barack Obama to the Middle East to seek a ceasefire, Kerry held talks on Tuesday in Cairo with Egyptian Foreign Minister Sameh Shukri.
"There is a framework ... to end the violence and that framework is the Egyptian initiative," Kerry said at a joint news conference with Shukri.
"For the sake of thousands of innocent families whose lives have been shaken and destroyed by this conflict, on all sides, we hope we can get there as soon as possible," he said.
Egypt was key to securing an end to a previous bout of Gaza fighting in 2012, but the country's new leadership is openly hostile to Hamas, potentially complicating the negotiations.
"We hope (Kerry's) visit will result in a ceasefire that provides the necessary security for the Palestinian people and that we can commence to address the medium and long-term issues related to Gaza," Shukri said.
With the war on Gaza entering its third week, the Palestinian death toll rose to 608, including nearly 100 children and many other civilians, Gaza health officials said.
The Israeli military said it had killed 183 militants.
Twenty-nine Israelis, 27 of them soldiers, have died.
Kerry said the United States would provide $47 million in humanitarian aid for Gaza.
Officials said he might travel to Qatar, a Gulf state which has relatively close ties to Hamas and hosts its leader, Khaled Meshaal.
Palestinian civilians in densely-populated Gaza have no place to hide from Israel's military offensive and children are paying the heaviest price, the United Nations said on Tuesday.
"There is literally no safe place for civilians," Jens Laerke, spokesman of the UN Office for Humanitarian Assistance (OCHA), told a news briefing in Geneva.
With Israeli shells and bombs hitting Gaza day and night, thousands of people have fled districts close to the border. The main UN agency in Gaza, UNWRA, said almost 102,000 people had taken shelter in 69 of its schools.
Israel has signalled it is in no hurry to achieve a truce before reaching its goal of crippling Hamas's militant infrastructure, including rocket arsenals and networks of tunnels.
Hamas has set a number of demands before a truce could be reached, including that Israel and Egypt lift their debilitating 7-year-old blockade of Gaza and its 1.8 million people, and that Israel release several hundred Palestinians detained during a search last month for three Jewish teenagers later found dead.
Livni said the Hamas demands were unacceptable to both Israel and Egypt.