Israel kept commercial border crossings with the coastal territory closed for a 10th day, citing cross-border rocket attacks by Gaza militants.
"We have run out this evening and unless the crossing points open ... we won't be able to get that food into Gaza," said John Ging, a top official with the United Nations Relief and Works Agency (UNRWA).
Ging called the economic situation in Gaza "a disaster."
UNRWA officials said the agency distributed food parcels to Gaza residents on Thursday but was suspending further deliveries because of a shortage of supplies.
Israel had initially said it would allow the delivery on Thursday of some 30 trucks of food and other humanitarian goods into the enclave, where a flare-up in cross-border fighting threatens a 5-month-old truce along the Israel-Gaza frontier.
Israeli Defense Ministry spokesman Peter Lerner blamed "continued rocket fire and security threats at the crossings" for the decision to block the shipments.
Also on Thursday, Israel held up deliveries of European Union-funded fuel to the territory's sole power plant. Palestinian officials said the facility would be shut down later in the day.
'Ceasefire faltering but not over'
Some 1.5 million people live in the Gaza Strip, where residents said food remained available but certain items were in short supply. Some 750,000 Gaza residents, most living in refugee camps, depend on UNRWA food supplies.
UNRWA head Karen AbuZayd told Reuters in an interview in Brussels she was worried Israel was narrowing the criteria for humanitarian aid and that certain items, including some school supplies, would be excluded from future shipments.
Palestinian militants fired several rockets at southern Israel earlier on Thursday, causing no casualties, the Israeli army said. The salvoes came a day after soldiers killed four Hamas gunmen during a raid into the Gaza Strip.
Israel says it remains committed to the Egyptian-brokered ceasefire, which went into effect on June 19.
"Without a doubt, it is faltering, but it isn't over," Israeli Deputy Defense Minister Matan Vilnai told Israel Radio.
Israel has not allowed the UN and other agencies to bring supplies into the Gaza Strip since Nov. 4, when its troops raided the territory to destroy what the army described as a tunnel built by militants to kidnap Israeli soldiers.
Six Hamas gunmen were killed in the raid. Militants responded to the incursion with rocket salvoes.
The ceasefire calls on Hamas to halt rocket fire and other attacks against the Jewish state. It also demands that Israel gradually lifts its blockade of the Gaza Strip.
Israel tightened the blockade of Gaza after Hamas Islamists seized the territory a year ago from rival Fatah forces royal to President Mahmoud Abbas.