"Medicines, foodstuffs, energy, all will be reaching the Gaza Strip in the volume that is required and in an expeditious manner."
Speaking at an Arab League summit in Kuwait, Palestinian Authority President Mahmoud Abbas called for the formation of a national unity government in the Palestinian territories, along with simultaneous parliamentary and presidential elections.
Correspondents say Mr Abbas is facing challenges to his legitimacy, with Hamas claiming his term is over and many of his supporters angered by criticisms he made of the militant group while it was under fire from Israel.
Previous talks on a unity government have broken down, and the two sides remain divided over the timing of possible elections.
The league is expected to discuss a proposal for a $2bn (£1.3bn) fund for reconstruction in Gaza. Saudi King Abdullah said his country would donate $1bn.
Correspondents say the summit was supposed to focus on economic reform, but has been overshadowed by the Gaza crisis and the divided political response of Arab leaders.
Israel says it is not interested in staying in Gaza
Egypt's President Hosni Mubarak accused Hamas of inviting the Israeli offensive by not extending a six-month ceasefire - brokered by Egypt - when it expired last month.
Meanwhile, Israeli Prime Minister Ehud Olmert said he wanted troops to leave as quickly as possible, and some have already left.
The BBC's Christian Fraser, on the road from Rafah in the south to Gaza City in the north, says the troops are pulling out fast.
Traffic jams are building up, as people try to get to Gaza City to reunite with friends and relatives, he says, while Hamas fighters stride confidently down the road with rifles slung across their shoulders.
Israel called a ceasefire on Saturday, saying it had met its war aims.
Hamas later declared its own truce with one of its leaders claiming a "great victory" over Israel and saying its ability to fire rockets had not been affected by the Israeli strikes.
The BBC's Bethany Bell in Jerusalem says many people face shortages of food, medicine and fuel.
Mr Ging, director of operations for the UN agency for Palestinian refugees (Unrwa), said most important was how to get basic supplies into Gaza.
"We have a big recovery operation ahead of us, reconstruction - none of it will be possible of course, on any scale, until we get crossing points open," he told the BBC.
Unrwa was keen to reopen its schools, Mr Ging said, where 50,000 people were sheltering. Tens of thousands have been made homeless by the bombardment.
Big questions remain, our correspondent says, such as who will police Gaza's southern border with Egypt and how much power Hamas still has.
At least 1,300 Palestinians, according to Palestinian sources, and 13 Israelis have been killed since Israel launched its offensive on 27 December. Palestinian medical sources say at least 95 bodies have been pulled from the rubble since Israel halted its assault.
Correspondents say the ceasefire in Gaza remains fragile, although no air strikes, rocket attacks or major clashes were reported overnight.
Palestinian militants fired about 20 rockets over the border after the Israeli ceasefire announcement, and Israel responded with an air attack.
Surrounded by an array of European political leaders, some of whom were highly critical of Israel's tactics in the conflict with Hamas, the Israeli prime minister said his country was not interested in staying in the Gaza Strip.
"We didn't set out to control Gaza, we don't want to remain in Gaza and we intend on leaving Gaza as quickly as possible," he said.
Israelis and Palestinians give their views on Israel's ceasefire announcement
Anonymous Israeli officials, quoted by AP news agency, said the withdrawal would be completed before US President-elect Barack Obama's inauguration on Tuesday.
Correspondents say Israeli leaders want to get off to a smooth start with the new administration in Washington.
The European leaders had travelled to Israel to lend their support to the ceasefires.
The top Hamas leader in Gaza, Ismail Haniya, said Israel had "failed to achieve its goals".
In a speech broadcast on Hamas TV, he said: "God has granted us a great victory, not for one faction, or party, or area, but for our entire people."
Hamas said it would hold fire for a week to give Israel time to withdraw its forces from the Gaza Strip.
A spokesman for Hamas' military wing, Abu Ubaida, said its rocket capabilities had not been affected by the conflict.
"We hereby stress that our rockets are being developed and are piling up, and that the enemy will receive more rockets and God willing, our rockets will hit more targets," he said in a news conference broadcast live on Hamas' al-Aqsa TV.
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