The threat of a wider conflict arose when militants in Lebanon fired two rockets into northern Israel.
One rocket crashed into a retirement home, but there were no serious injuries. Israel responded with mortar shells.
The driver of the UN truck died immediately; another worker in the truck died later of his wounds. The truck, which came under fire in northern Gaza, was marked with the UN flag and insignia.
During a three-hour pause in the fighting to allow in food and fuel and let medics collect the dead, nearly three dozen bodies were found beneath the rubble of bombed out buildings in Gaza City.
Many of the dead were in the same neighbourhood where the international Red Cross said rescuers discovered young children too weak to stand who had stayed by their dead mothers. The aid group accused Israel of an "unacceptable" delay in allowing workers to reach the area.
Relations between Israel and humanitarian organisations have grown increasingly tense as civilian casualties have mounted.
The United Nations demanded an inquiry this week after Israeli shells killed nearly 40 Palestinians near a U.N. school filled with Gazans. Israel said militants had launched an attack from the area, then ran into a crowd of civilians for cover.
The 13-day Israeli offensive has killed about 750 Palestinians, according to Palestinian hospital officials and human rights workers. Two Israeli soldiers were killed in combat Thursday, raising the number of soldiers killed in Gaza to eight since the assault began December 27. Four Israelis, including one soldier, also have been killed by rockets fired at Israeli cities.
"We've been coordinating with them (Israeli forces) and yet our staff continue to be hit and killed," said a UN.spokesman, Chris Gunness, announcing the suspension. The UN is the largest aid provider in Gaza.
Israeli police, meanwhile, said militants in the Gaza Strip fired 24 rockets into Israel on Thursday, injuring four people, one of them seriously. Militants fired larger numbers of rockets in the early days of the conflict.
The Israeli assault is intended to halt years of Palestinian rocket attacks on southern Israel. But with roughly half the Palestinian dead believed to be civilians, international efforts to broker a cease-fire have been gaining steam.
Israeli envoys traveled to Egypt on Thursday to discuss the proposal being brokered by France and Egypt.
French President Nicolas Sarkozy said any time lost will play into the hands of those who want war.
"The weapons must go quiet, the escalation must stop, Israel must obtain security guarantees and leave Gaza," he said in Paris.
The UN provides food aid to around 750,000 Gaza residents - about half of Gaza's population - and runs dozens of schools and clinics throughout the territory. They have some 9,000 local staffers in Gaza as well as a small team of international staffers.
Elena Mancusi Materi, UNRWA's spokeswoman in Geneva, said the suspension concerned all truck movement in Gaza.
"If someone comes to one of our food distribution centers, we will give that person food," she said.
"If people come to our clinics with injuries, we will treat them."
For a second straight day, Israel suspended its Gaza military operation for three hours to allow in humanitarian supplies. Shortly before the pause took effect, the U.N. said one of its aid trucks came under fire from a gunner on an Israeli tank, killing the driver.
UN spokesman Adnan Abu Hasna said the U.N. coordinated the delivery in northern Gaza with Israel, and the vehicle was marked with a UN flag and insignia. The Israeli army said it was investigating.
Hasna said the truck driver died immediately and another man in the truck died later of his wounds. A third man was also injured.
In Geneva, the international Red Cross said it would restrict its aid operations to Gaza City for at least one day after one of its convoys came under Israeli fire at the Netzarim crossing during the pause in fighting Thursday. One driver was lightly injured.
Dr. Moaiya Hassanain of the Palestinian Health Ministry said 35 bodies were discovered Thursday during the three-hour lull in several areas around Gaza City that have seen fierce fighting between Israeli troops and Hamas militants.
He said it was unclear how many militants were killed because the remains were in poor condition, but that women and children were among the dead. Hassanain said 746 Palestinians have died in the Israeli offensive.
Many of the dead found Thursday were in Gaza City's Zeitoun neighborhood, where the international Red Cross said it found four small children alive next to their mothers' bodies in the rubble of a home hit by Israeli shelling. The aid group says 15 dead were recovered from two houses in Zeitoun on Wednesday.
A Red Cross spokesman says rescuers had been refused permission by Israeli forces to reach the site for four days. It said the delay was "unacceptable."
The Red Cross statement was a rare public criticism from the aid group, which normally conducts confidential negotiations with warring parties.
The Israeli military said in a statement that Hamas militants used Palestinian civilians as human shields, and that Israeli forces work closely with aid groups to help civilians in Gaza.
In other Gaza violence, Israel attacks killed at least 24 Palestinians Thursday, including the U.N. driver, according to Hassanain.
The rockets from Lebanon raised the specter of renewed hostilities on Israel's northern frontier, 2½ years after Israel battled the Hezbollah guerrilla group to a 34-day stalemate. War broke out between Hezbollah and Israel in 2006 as Israel battled Palestinian militants in Gaza, on Israel's southern borders.
No group claimed responsibility. Lebanon's government condemned the attack, and Hezbollah - which is now part of Lebanon's government - denied any responsibility for the rocket fire, which lightly injured two Israelis at a retirement home.
"The rocket entered through the roof, hurling the water heaters into the air. It went through bedrooms upstairs and then into the kitchen," said Henry Carmelli, the home's manager.
Israel has repeatedly said it was prepared for a possible attack on the north since it launched its campaign against Hamas militants in Gaza. Israel has mobilised thousands of reserve troops for such a scenario, and leaders have warned Hezbollah of dire consequences if it enters the fighting.
"We are prepared and will respond as necessary," Defense Minister Ehud Barak said.
The Israeli offensive has reduced Palestinian rocket fire, but not stopped it. Several barrages were reported on Thursday, including one strike that damaged a school and sports center in the southern city of Ashkelon, police said. Both buildings were empty.
For Israel to accept a proposed cease-fire deal, "there has to be a total and complete cessation of all hostile fire from Gaza into Israel, and ... we have to see an arms embargo on Hamas that will receive international support," said government spokesman Mark Regev.
Hamas said it would not accept a truce deal unless it includes an end to the Israeli blockade of Gaza - something Israel says it is not willing to do. Israel and Egypt have maintained a stiff economic embargo on Gaza since the Hamas takeover in June 2007.
The Palestinian Authority controls the West Bank while Hamas rules Gaza - territories on opposite sides of Israel that are supposed to make up a future Palestinian state.
