All reports indicate that there are sufficient medicine and food in Gaza, the statement read.
The UN's Maxwell Gaylard said: "It is true supplies have been going into the Strip, in fact possibly more than in previous weeks, but at the same time there are critical gaps."
A leading international charity, Oxfam, which has a programme in Gaza, warned the situation "is getting worse by the day", with clean water, fuel and food in short supply.
It said hospitals were overwhelmed with casualties, and reported that raw sewage was pouring into the streets in some areas.
Israel tightened its control of what gets in and out of the crowded coastal Strip after Hamas, the elected power, seized control of the area from rival Fatah forces 18 months ago.
Since then, the UN says there has been a significant deterioration in infrastructure and basic services, with 80% of the 1.4m population unable to support themselves.
Israeli planes attacked the homes of more than 20 leading Hamas figures on Friday, UN officials said.
There was also an air strike on a mosque, which the Israelis said served as a command post.
ROCKET ATTACKS FROM GAZA
Since the start of Israel's operations in Gaza, Israeli sources say Palestinian militants have fired the following:
27 December 2008: 61 rockets, 33 mortar shells
28 December: 14 rockets, 16 mortar shells
29 December: 57 rockets, 15 mortar shells
30 December: 42 rockets, 6 mortar shells
31 December: 43 rockets, 25 mortar shells
Source: Intelligence and Terrorism Information Center, Israel
Earlier in the day, five Palestinians, including three children, were killed in an Israeli strike. The Israel Defense Forces have attacked more than 500 Hamas targets in Gaza since the campaign began.
To date, some 2,000 Palestinians have been wounded, according to the UN.
Palestinian militants continued to fire on Israel, launching more than 60 missiles in 24 hours. Four people were injured in the southern Israeli city of Ashkelon.
Four Israelis have died in the rocket attacks Israel is trying to prevent.
Hamas leader-in-exile Khaled Meshaal said Israel faced a "black destiny" if it launched a ground offensive.
In a pre-recorded statement broadcast on al-Jazeera television, he said Israelis would be making a "stupid mistake", adding that Hamas resistance and infrastructure were intact.
"We will not break, we will not surrender or give in to your conditions," Mr Meshaal said in Syria.
The US Secretary of State, Condoleezza Rice, called for a "durable and sustainable" ceasefire - one which should "not allow a re-establishment of the status quo ante, where Hamas can continue to launch rockets out of Gaza".
The BBC's Kim Ghattas in Washington says it is unclear what Ms Rice means by "sustainable ceasefire" or how it can be attained.
But it is a position that is widely interpreted as tacit backing by Washington for Israel to continue its military operation and try to weaken Hamas as much as possible, our correspondent says.
Meanwhile, thousands of Palestinians in the West Bank joined demonstrations on Friday after a call from Hamas for a "day of wrath" against the Israeli attacks on Gaza.
Palestinian youths clash with Israeli security forces in East Jerusalem
Correspondents say protesters were directing their anger not just at Israel but at Arab governments and their own leaders for their failure to stop the offensive.
Huge crowds gathered in Ramallah, while in Israeli-occupied East Jerusalem, youths threw stones at security forces, who fired tear gas.
Demonstrations were also held across the Middle East and in several Asian countries, as well as in Australia and Kenya.
The protests were called after an Israeli air strike hit the home of Nizar Rayyan, a firebrand leader of Hamas who refused to go into hiding, killing him and members of his family.
In a separate development, about 100 foreign passport holders - mainly women married to Palestinians, and their children - were allowed by Israel to leave Gaza. Correspondents say it is being seen as a possible last move before Israeli tanks roll in.
BBC Middle East Editor Jeremy Bowen says a week of bombardment has not been able stop the rocket fire, and Israel now has to decide whether to send in ground troops.
Israel is refusing to let international journalists into Gaza, despite a Supreme Court ruling to allow a limited number of reporters to enter the territory.
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