The head of the main United Nations agency supporting Palestinian refugees has warned that the organisation is facing the most severe funding crisis in its history, threatening its support to an estimated 5.3 million people, including more than 400,000 inside Syria.

Pierre Krähenbühl, commissioner general of the UN Relief and Works Agency, added that cuts in support to the already impoverished and demoralised population his organisation supports – many of them victims of recent conflict – risked radicalising a new generation of young Palestinians.

The UNRWA, which provides education, medical care and emergency assistance to Palestinian refugees, is facing a shortfall of almost one-third of its budget, in large part because of the Trump administration’s decision to withhold much of its funding.

Krähenbühl told the Guardian the agency had managed to persuade some of its key donors – including the UK – to fast-track money promised to keep its core education and health services funded until early summer. But he said money for emergency cash assistance to provide food aid for 1 million people in Gaza and, crucially, 400,000 in Syria, would run out within weeks.

In the absence of a permanent peace deal, the UNRWA – which was founded in 1949 to provide temporary aid to 750,000 Palestinians displaced in the conflict surrounding the foundation of Israel – supports a body of refugees that has now swollen to roughly 3.5 million.

The stark warning was delivered as Krähenbühl revealed that last month’s UNRWA emergency appeals for Syria and the Occupied Palestinian Territories (in addition to the organisation’s budget for core services in education, health, relief and social services) – aimed at plugging a $500m (£356m) deficit – had so far raised only $1m.

The US announced it was cutting funds to the UNWRA earlier this year in the fallout from a UN general assembly vote that overwhelmingly rejected Donald Trump’s decision to recognise Jerusalem as the capital of Israel.

If you want to ask us how to avoid radicalising Palestinian youth then it is not by cutting $300m of our funding Pierre Krähenbühl, UNWRA

Speaking to the Guardian during a visit to London to brief Foreign Office minister Alistair Burt, Krähenbühl ascribed the funding gap affecting the UNRWAto an existing shortfall and new US cuts.

“Last year, the US provided $364m. This year it has announced only $60m,” he said, adding that the money that Washington had agreed to provide this year could not be spent helping Syrian refugees in Lebanon and Syria.

“We are used to dealing with funding crises,” he added, referring to the most recent, when the agency come close to closing its schools in 2015, “but this is the biggest and most severe in our history.”

“I have just come from the Munich security conference. At every seminar, people were asking the same question: about security and how we combat radicalisation. If you want to ask us how to avoid radicalising Palestinian youth, then it is not by cutting $300m in our funding.”

The UNRWA is despised by some on the Israeli right and their supporters in the US, who accuse the organisation of perpetuating Palestinian refugee populations. But UNRWA officials, including Krähenbühl, argue that their work preserves stability in substantial refugee populations from Gaza to Jordan and Lebanon, as well as in Syria and the West Bank.

“If you put aside the fact these are refugees with human rights and look at this in purely transactional terms,” he said, referring to how Trump’s outlook on policy is widely interpreted, “then UNRWA offers the best deal. We fund a stable education system which, if it were in the US, would be the third largest after New York and Los Angeles.”

Often sidelined in the heated discussions about the UNRWA’s work, its support of Palestinian refugees in Syria has become increasingly critical during the war there, maintaining about 47,000 children in education. Broadcast content produced in Gaza has been an important element of the organisation’s educational support.

“Most of the Palestinian refugees in Syria were largely economically self-sufficient before the war,” explained Krähenbühl, who said that many were now dependent on the UNRWA for money to buy food.

January’s decision to reduce US funding of the UNRWA came amid evidence of splits over the approach within the Trump administration. The secretary of state, Rex Tillerson, along with national security adviser HR McMaster and defence secretary Jim Mattis, were more convinced of its utility against the hostility of Trump than Nikki Haley, his combative and fiercely pro-Israel UN ambassador, who has led the charge against it.

“We made it clear that it was a pledge, it was not a guarantee, and that it would need to be confirmed later. At this time, we will not be providing that,” US State Department spokeswoman Heather Nauert said at the time, adding that the US was tired of being the largest donor to the UNRWA and wanted other countries to step up to the table.