As fuel runs out, residents are scrambling for basic necessities.
People are stocking up on fuel and food before prices spike and supplies run dry.
The UN has said Israel should not collectively punish Gaza's population while responding to security threats.
The organisation has criticised Israel's decision to close border crossings into Gaza, preventing aid deliveries to the 1.5 million people living in the territory, saying on Saturday that the move could provoke a humanitarian crisis.
He called for "maximum restraint on the part of the Israel defence forces".
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"Such action cuts off the population from much-needed fuel supplies used to pump water and generate electricity to homes and hospitals," Ban Ki-moon, the UN secretary-general, said.
Ban also urged an immediate end to violence in Gaza and Palestinian sniper and rocket attacks into Israel.
John Holmes, the UN undersecretary-general for humanitarian affairs, said: "We all understand the security problems and the need to respond to that but collective punishment of the people of Gaza is not, we believe, the appropriate way to do that."
Holmes said the Israeli response was unwarranted.
"This kind of action against the people in Gaza cannot be justified, even by those rocket attacks," he said.
Al Jazeera's Jacky Rowland, reporting from Gaza, says that electricity is running out fast.
| A lack of fuel will lead to a shortage of|
basic necessities [AFP]
She said: "The only power station in Gaza has already closed down half its power generating capacity. The final generating unit is set to close in a matter of hours."
"No fuel coming in means no power generation, it also means no fuel for the generators that fuel the water pumps - a lot of the water in Gaza is deep beneath the surface, and it has to be pumped to the surface - so no fuel can also mean no water."
Rowland also said that international condemnation highlights the need for Israel to stop its collective punishment of residents in Gaza.
She said: "Fighters make up about one per cent of the population.
"There are over 1 million people that live in the Gaza Strip, and it is unacceptable that they are all suffering for the actions of a small minority."
Holmes said he worried the violence in Gaza could spin out of control, making a dire humanitarian situation even worse.
"I believe it is a [humanitarian] crisis already," he said.
Israel has continued to push ahead with its military offensive against Palestinian fighters in both Gaza and the West Bank.
On Thursday, Ehud Olmert, the Israeli prime minister, said in a statement that his country was at "war" against fighters in the Gaza Strip.
The Israeli military has particularly intensified its operations in Gaza, with at least 32 people killed during the past week. In response, Hamas has begun firing rockets at Israel for the first time in months.
Around 230 rockets and mortars have been fired over the border since Tuesday, the Israeli military said.
On Saturday, a pre-dawn Israeli air strike north of Gaza City killed at least two Hamas fighters on Saturday, medics said.
The two men were in their 20s and members of the Ezzadine al-Qassam Brigades, the armed wing of Hamas, the medics said.
A third Hamas fighter died on Saturday from wounds suffered in an air strike on Thursday.
Later in the day, hundreds of Palestinians attended the funerals of the dead fighters.
An Israeli military spokeswoman said fighter jets carried out two strikes in northern Gaza on Saturday targeting rocket launchers, but would not specify where they took place.
Israeli soldiers also captured four Hamas fighters, and took them to Israel for questioning, according to the spokeswoman.
Hamas said the Israeli troops also arrested family members of the fighters.
More than 38 Palestinians have now been killed since Monday.
Israel bombed four other targets in Gaza on Friday - including a Hamas government building.
The office block in a crowded part of the city was reduced to rubble, killing one woman and injuring almost 50 other people.
Source: Al Jazeera and agencies