The agency has fired several staff over Israel's accusations and promised a thorough investigation into these claims, which were not specified.
Several countries, including the United States, France, Britain, Germany and Japan, have announced the suspension of further funding to the agency.
In the southern city of Rafah, where 1.5 million displaced people have taken refuge, Gazans told AFP that the support they received from the agency amounted to a lifeline.
"We live on aid from UNRWA. If it stopped, we would die of hunger, and no one would look at us," said Sabah Musabih, 50.
Amal Abdel Moneim, a refugee from Gaza City in the north, said there were no other organisations offering help.
"Our people are supported by no one except UNRWA," he said.
"If UNRWA stops supporting us, our people will be lost and dead."
The October 7 Hamas attack resulted in about 1,140 deaths, mostly civilians, in southern Israel, according to an AFP tally of official figures.
Militants also seized 250 hostages, of whom Israel says around 132 remain in Gaza, including the bodies of at least 28.
Israel's relentless military offensive has killed at least 26,637 people in Gaza, most of them women and children, according to the Hamas government's health ministry in the territory.
Israel has vowed to stop the agency's work in Gaza after the war.
Israeli Foreign Minister Israel Katz said Monday he had cancelled a meeting with UNRWA head Philippe Lazzarini scheduled for later in the week.
"Lazzarini should draw conclusions and resign," Katz posted on X, formerly Twitter.
An UNRWA source told AFP that the suspension of funding announced by several countries had yet to have an effect on the ground.
"There is no change in the aid distribution mechanisms implemented by UNRWA in the Gaza Strip," the source said on condition of anonymity as he was not supposed to talk about the sensitive issue.
"The situation is very dangerous, and if the United States and the supporting countries insist on stopping their support for UNRWA, this will be a major disaster," the source said.
While Washington has announced it had stopped funding the agency, it was still weighing options for the future.
UNRWA has "literally helped save thousands of lives" in Gaza, US National Security Council spokesman John Kirby told CNN on Monday.
"So while this is very serious, and it needs to be taken that way, I think we also need to remember not to impugn the good work of the entire agency."
