Yemen's Houthi rebels on Tuesday said they were surprised by accusations from the United Nations food agency that they are stealing "from the mouths of hungry people" by diverting food deliveries.

Mohammed Ali al-Houthi, head of the Supreme Revolutionary Council, said in a statement that the rebels were taken aback by the World Food Program 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," he said.

The World Food Program on Monday threatened to suspend some aid shipments to Yemen if the Houthi rebels do not investigate and stop theft and fraud in food distribution, warning that the suspension would affect some 3 million people.

Al-Houthi said WFP "did not communicate officially" with the rebels regarding the alleged theft of aid, adding that making the critical comments to the media is considered "a major deviation in the work of the program."

He called on the WFP to back up its accusations with proof.

Al-Houthi also accused the U.N. agency of sending "rotten food" to the war-torn country, saying Yemen refused to allow that food in because "it violates standards and regulations and is not suitable for human consumption."

The rebel leader also accused U.N agencies of being biased.

"The work of these organizations is mostly politicized ... and this situation reflects that their work has shifted from independent to subordinate to the United States and Britain," he said.

The World Food Program's ultimatum was an unprecedentedly strong warning, pointing to how corruption has increased the threat of famine in Yemen, where a four-year civil war has created the world's worst humanitarian crisis.

In a letter sent to rebel leader Abdul-Malek al-Houthi, WFP director David Beasley 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 3 million people," the letter said. "This criminal behavior must stop immediately."

The Iran-aligned Houthis, who control much of northern Yemen, have been at war with a U.S.-backed and Saudi-led coalition since March 2015. The fighting has killed tens of thousands of people, and has driven the Arab world's poorest country to the brink of famine, with millions suffering from extreme hunger. The U.N. calls it the world's worst humanitarian disaster.

The Associated Press reported 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. Some groups are blocking deliveries to communities they view as enemies.

The WFP said it obtained photographic evidence showing rebels seizing food and manipulating lists of aid recipients.

The U.N. agency helps about 8 million hungry people in Yemen and has been working to increase its scope to reach a total 12 million. It wants an overhaul of the relief system, including biometric registration, but says the rebels resist such measures.

WFP's accusation came as a U.N. team led by a Dutch officer has been monitoring a cease-fire in the Red Sea port city of Hodeida since late December, which ended months of fierce fighting between the two sides for control of the city. Some 70 percent of Yemen's imports come through Hodeida.