A large part of the food aid meant to help residents in the capital Sanaa has not reached them, the Rome-based WFP said in a statement.

Instead, reports had established some of the food had been put on sale in Sanaa markets by a rebel-controlled organisation which the WFP had entrusted to distribute the aid in the city.

The WFP said similar cases had been reported in other areas of the country controlled by the rebels.

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

He also called on the Houthi authorities "to take immediate action to end the diversion of food assistance."

"Unless this happens, we'll have no option but to cease working with those who've been conspiring to deprive large numbers of vulnerable people of the food on which they depend," he said.

The Iran-backed Houthi rebels and the Saudi-supported government agreed a ceasefire which went into effect on December 18 but tensions remain high amid charges of bad faith by both sides.

Years of civil war have devastated Yemen, leaving perhaps 20 million people in need of food aid, according to the UN.