UN chief António Guterres has urged countries that halted funding for the UN agency for Palestinian refugees, UNRWA, to continue its operations.
"The dire needs of the desperate populations they serve must be met," Mr Guterres said.
Nine countries, including the UK, have taken action since Israel told UNRWA some staff were involved in the 7 October deadly Hamas attacks on Israel.
The agency says it is investigating and has already sacked some employees.
The countries that have now suspended funding UNRWA are Australia, Canada, Finland, France, Germany, Italy, the Netherlands, the UK and the US.
Created in 1949, the United Nations Relief and Works Agency, UNRWA, is the biggest UN agency operating in Gaza. It provides healthcare, education and other humanitarian aid to Palestinians in Gaza, the West Bank, Jordan, Lebanon and Syria. It employs around 13,000 people inside Gaza.
Since Israel began its offensive in response to the Hamas attacks UNRWA has used its facilities across Gaza to shelter hundreds of thousands of displaced civilians.
Israel has long accused different branches of the UN - including UNRWA - of bias and even of antisemitism.
Details about the Israeli allegations have not been made clear, but reports in the Israeli media suggest UNRWA vehicles and facilities may have been used for the attack in which Hamas gunmen killed around 1,300 people, mostly civilians, and took another 240 hostage.
An adviser to Israeli Prime Minister Benjamin Netanyahu on Friday told the BBC that the 7 October Hamas attacks had involved "people who are on their [UNRWA] salaries".
Mr Regev also referred to an Israeli hostage who, on her release, said she had been "held in the house of someone who worked for UNRWA".
In his statement on Saturday, the UN secretary general said that Israel had made allegations against 12 UNRWA employees - nine had been sacked, one had died and the identity of the remaining two was being "clarified".
Mr Guterres said that he understood the concerns of the governments which have suspended funding. "I was myself horrified by these accusations," he said, adding that "the abhorrent alleged acts of these staff members must have consequences".
But this should not mean that the many thousands who work for the agency should be penalised, the UN chief said.
Mr Guterres's statement followed a strongly-worded reaction by the head of UNRWA, Philippe Lazzarini, who called the decision to suspend funds "shocking" given the small number of staff facing the Israeli allegations.
He made it clear that UNRWA shared the list of its staff with Israel every year and had never received any concerns.
Some countries have said they will continue their support for UNRWA. Norway's representative to the Palestinian Authority said the organisation has a "crucial role" in distributing aid, and emphasised the "need to distinguish between what individuals may have done, and what UNRWA stands for".
Israeli Foreign Minister Israel Katz urged Mr Lazzarini to resign and said he aimed to stop UNRWA operating in Gaza after the war.
The 7 October attacks triggered Israel's massive retaliation on Hamas in Gaza - air strikes and shelling that have killed more than 26,000 Palestinians, according to the territory's Hamas-run health ministry.
UNRWA says it is struggling to get humanitarian aid to many of the estimated 1.7 million people - nearly three-quarters of the population - displaced by 12 weeks of fighting.
Most recently, the fighting has centred on Khan Younis, where thousands of Palestinians displaced from the north had congregated.
Many are now said to be moving further south, towards Rafah on the border with Egypt.
Most of northern Gaza has been reduced to ruins as Israel pursues its campaign with the stated aim of eliminating Hamas.
Israel says it is destroying a network of tunnels - with estimates that 20-40% had been made unusable so far, according to US and Israeli officials quoted by US newspaper Wall Street Journal.