Almost 800 Palestinians are thought to have died in the two-week conflict
The UN aid agency Unrwa is to resume operations in Gaza as soon as possible after receiving assurances on safety from Israel, a spokeswoman said.
It comes a day after Unrwa suspended deliveries in Gaza because staff there had been hit in Israeli attacks.
Both Israel and Palestinian militant group Hamas have so far ignored a UN resolution calling for an immediate end to two weeks of conflict.
Israel says its military offensive is intended to stop rocket fire from Gaza.
A number of rockets were fired into southern Israel on Friday but there were no reports of casualties.
The Israeli air force continued to hit what it said were Hamas targets in Gaza.
Late on Friday, UN Secretary General Ban Ki-moon telephoned Mr Olmert to express his disappointment that violence was continuing on the ground in disregard of the ceasefire call, his spokeswoman said.
Earlier, Israeli Prime Minister Ehud Olmert said the continued rocket attacks on Israel showed the resolution was "unworkable".
Officials in Mr Ehud's office were quoted as saying "the Israeli military will continue to protect Israeli civilians and carry out its missions".
Hamas said it had rejected the UN's call for an immediate ceasefire because it had not been consulted on the resolution and it was not in the interests of the Palestinian people.
But there were some signs of diplomatic movement. A Hamas delegation has gone to Cairo for Egyptian-hosted negotiations on a truce with Israel.
Palestinian leader Mahmoud Abbas is already in Egypt to discuss plans to end the fighting; German Foreign Minister Frank-Walter Steinmeier is also due arrive in the region on Saturday.
Announcing that aid efforts would resume, UN spokeswoman Michele Montas said the Israeli military had given "credible assurances that the security of UN personnel, installations and humanitarian operations would be fully respected".
As a result, Unrwa would resume its work as soon as possible, she said.
The agency suspended its operations in Gaza on Thursday after it said one person had been killed when a fork-lift truck on an aid mission came under Israeli tank fire at Gaza's Erez crossing.
Separately, UN High Commissioner for Human Rights Navi Pillay said an alleged failure of the Israeli military to help wounded civilians in Gaza could constitute a war crime.
On Thursday, the International Committee of the Red Cross (ICRC) said its staff had found four weak and scared children beside their mothers' bodies in houses hit by shelling in the Zeitoun neighbourhood of Gaza City.
Ms Pillay told the BBC: "The incident the Red Cross describes is very troubling because it has all the elements of what constitutes a war crime.
"There is an obligation to protect the wounded, to treat the sick, to remove them to safety and here, according to the Red Cross, Israeli soldiers just stood by and did nothing for these four children and one adult who were too weak to move."
The UN human rights body has demanded that human rights monitors be deployed in Gaza, Israel and the West Bank so that any violations of international law can be documented independently.
Asked whether Israel was living up to its human rights obligations, US Secretary of State Condoleezza Rice said it was hard for Israel to safeguard civilians because Gaza was very densely populated.
Israel paused its military operations for three hours in the afternoon to allow supplies to be brought in for Gaza's residents.
However, Israeli army spokesman Capt Eli Isaacson told the BBC that during that period, two rockets had been fired from Gaza towards Israel and that Israeli forces had returned fire.
Gaza health officials say about 800 Palestinians have been killed since the current conflict began on 27 December.
Thirteen Israelis had died as of Thursday, according to the Israeli military.
Fourteen out of 15 Security Council members backed the resolution on the Gaza crisis, with the US abstaining.
The motion called for an "immediate, durable and fully respected ceasefire" leading to the "full withdrawal" of Israeli forces from Gaza.
It also demanded "the unimpeded provision and distribution throughout Gaza of humanitarian assistance", measures to prevent arms smuggling to Palestinian militants and the opening of border crossings into Gaza.
Israel wants to stop rocket attacks on southern Israel and to stop Hamas smuggling weapons into Gaza via Egypt, while Hamas says any ceasefire deal must include an end to Israel's blockade of Gaza.