(CNN) The United Nations is threatening to suspend aid that helps thousands of destitute Yemenis following a CNN investigation that exposed the theft or "diversion" of food aid by Houthi rebels.

David Beasley, head of the UN's World Food Programme (WFP), told CNN's Becky Anderson that up to $15 million worth of food a month was not making it to the desperate people for whom it was intended.

Children are dying as a result, he said, and his organization had to "hold strong" to try to get a breakthrough.

CNN's weekslong undercover investigation inside Yemen found documents indicating families had received aid when they said they had not, as well as entire villages where no supplies had made it through for weeks amid an ongoing spat between the WFP and the Houthi rebels who control much of the country.

Beasley said the WFP goal was to feed 12 million Yemenis this year, nearly half of the population, but the persistent theft of aid meant deliveries might have to stop if they cannot be monitored.

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