Houthi rebels have denied accusations by the World Food Programme (WFP) of stealing humanitarian aid in war-torn Yemen.

The Associated Press news agency reported on Monday that armed factions on both sides of the conflict are stealing much-needed food aid, diverting it to their fighters or reselling it for profit.

In a statement published on Tuesday, Mohamed Ali al-Houthi, head of the so-called "Supreme Revolutionary Committee", said his group was "surprised" by the WFP allegations.

"We were surprised by the statement of the WFP Executive Director, which included threats to stop supplying food for large numbers of needy people in Yemen," read the statement cited by the Houthi-linked al-Masirah website.

He said the WFP "didn't communicate" with the group regarding the alleged theft of aid, adding that "exporting this to the media is considered as a major deviation in the work of the programme".

On Monday, the WFP said it had collected evidence showing Houthi fighters diverted food shipments sent to ease the humanitarian crisis in Yemen to areas under their control.

"This conduct amounts to the stealing of food from the mouths of hungry people," WFP Executive Director David Beasley said in a statement.

"At a time when children are dying in Yemen because they haven't enough food to eat, that is an outrage. This criminal behaviour must stop immediately."

Beasley also said that a survey done by the agency showed that aid is only reaching 40 percent of eligible beneficiaries in the rebel-held capital, Sanaa. Only a third are receiving aid in the rebels' northern stronghold of Saada.

"If you don't act within 10 days, WFP will have no choice but to suspend the assistance ... that goes to nearly three million people," the letter said.

'Systematic misuse of food relief'

WFP is currently working to expand food aid operations to nearly 12 million hungry people in Yemen, the statement said.

Speaking to Al Jazeera, WFP spokesman David Orr said the organisation was "extremely concerned" by what they had discovered, and that there was an increase in selling food relief in Sanaa's markets.

"What we had been noticing looked like a systematic misuse of food relief," he said, speaking from Rome.

"To date, most of our investigations have been on the Houthi side in the capital Sanaa," he continued. "We've been effectively prevented from carrying out all the monitoring we would like."

"Where abuse and diversion of food aid is taking place, it means that it is not reaching those who desperately need it for survival," he added.

Yemen plunged into civil war in 2014 when Shia Houthi rebels overran much of the country, including the capital, Sanaa, forcing the government to flee to Saudi Arabia.

A year later, Saudi Arabia and several Arab allies launched a massive air campaign aimed at rolling back Houthi military gains.

The Saudi-led campaign in Yemen has devastated the country's infrastructure, including its health and sanitation systems, prompting the UN to describe it as one of the worst humanitarian disasters in modern times.