A three-day ceasefire in Gaza that has brought relief to millions entered its final stretch on Thursday with Israel ready to extend the calm but Hamas hedging its bets.
And US President Barack Obama put pressure on intensive ceasefire negotiations in Cairo by saying Gaza could not remain cut off from the world forever.
UN secretary general warned Britain, France and Germany meanwhile have put forward an initiative which would answer key demands on both sides and which has been presented to Israel, the Palestinians, Egypt and Washington, a diplomatic source said.
Four weeks of bloodshed between Israel and Hamas killed 1,886 Palestinians and 67 on the Israeli side.
With the ceasefire due to end at 0500 GMT on Friday, Egypt's intelligence chief Mohamed Farid Tohamy was to hold a new round of talks with each side later on Thursday, with the focus on extending the deadline.
An Israeli official has said Israel would be prepared to prolong the ceasefire "unconditionally".
But, following two-days of indirect Egyptian-brokered talks, Hamas said agreement had still not been reached to extend the calm which went into force on Tuesday.
"There is no agreement to extend the ceasefire," Hamas' exiled deputy leader Mussa Abu Marzuq wrote on Twitter.
With the guns silent, some semblance of normal life has returned to Gaza with traffic clogging the streets and people bustling about their business as shops, banks and markets resumed business.
In some areas, there were scenes of utter devastation, with certain districts reduced to an endless sea of rubble and shattered hulks of buildings, an AFP correspondent said.
A handful of men had camped out overnight in makeshift tents outside their ruins of what had once been their homes.
UN Secretary General Ban Ki-moon said that Gaza would be rebuilt -- but hopefully for the last time, as international patience showed signs of wearing thin.
"The senseless cycle of suffering in Gaza and the West Bank, as well as in Israel, must end," he said.
"Do we have to continue like this -- build, destroy, and build and destroy?
"We will build again but this must be the last time -- to rebuild. This must stop now."
- Gaza must be opened -
As the sides prepared for another round of talks in Cairo, Obama insisted that Gaza could not remain forever cut off by Israel's blockade, now in its eighth year.
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"Long-term, there has to be a recognition that Gaza cannot sustain itself permanently closed off from the world," Obama told a news conference in Washington.
"We're going to have to see a shift in opportunity for the people of Gaza," he said, adding that Palestinians needed to see "some prospects for an opening of Gaza so that they do not feel walled off and incapable of pursuing basic prosperity."
Lifting the blockade is the main Palestinian demand in the ceasefire talks in Cairo, while Israel has insisted Gaza be demilitarised.
Although Israel has expressed willingness to extend the truce indefinitely, there was no immediate word on its response to that and the other Palestinian demands.
"Today will be a crucial day," a member of the Palestinian delegation told AFP.
"If there is no Israeli response to the Egyptian initiative, which includes the Palestinian demands, then several options are open," he said.
"As for extending the truce, if it is proposed to us, we will think about it when the time comes, and that depends on how negotiations proceed today."
As the negotiations continued in Cairo, London, Paris and Berlin tabled an initiative offering an outline for rebuilding Gaza while ensuring Israel's security concerns were properly addressed, a diplomatic source said.
The proposal aims to strengthen the hand of Palestinian president Mahmud Abbas and his Palestinian Authority while clamping down on Gaza-based militant groups.
It proposes Abbas' security forces take control of border security in Gaza in conjunction with EU representatives and outlines a mechanism for preventing the rearming of militant groups in Gaza or the construction of new tunnels.
It also envisages opening the Rafah border crossing with Egypt then eventually opening other crossings to Israel. It also refers to the opening of a commercial port in Gaza, the source said.
- EU force at Rafah? -
In a related development, Israeli Foreign Minister Avigdor Lieberman called for EU "inspectors" to monitor Gaza's borders, Germany's mass-circulation Bild daily reported on Thursday.
Overnight, Lieberman also spoke with US Secretary of State John Kerry, denouncing Hamas for its intransigence over extending the ceasefire.
"Lieberman told Kerry that the Palestinian announcement from Cairo that they are not committing to extend the ceasefire is an act of blackmail which Israel will take into account," a statement from his office said.