Malnutrition is widespread in Yemen after four years of civil war, but the UN suspended deliveries of food aid to rebel-held areas of the country last month following accusations of "diversion of food."

The new agreement with the Huthis will allow food to be quickly delivered to the rebel-held capital Sanaa, though the two sides haven't formally inked the deal yet, WFP chief David Beasley told the UN Security Council.

"I can say that we have made substantial progress," he said during a meeting to discuss Yemen, in which he joined UN humanitarian officials in underlining the dire humanitarian situation in the country.

"Around 30 million people live in Yemen, and more than two-thirds of them are food insecure. That's 20 million women, men, boys and girls," he said.

While warning of a "dire and worsening humanitarian situation," UN envoy to Yemen Martin Griffiths said a fragile ceasefire in the key port of Hodeida "may finally allow us to focus on the political process before the end of this summer."

Mark Lowcock, the UN's humanitarian chief, said that international commitments of aid to Yemen weren't being honored.

He singled out Saudi Arabia and the United Arab Emirates, members of the coalition that intervened in Yemen in support of its government.

"Those who made the largest pledges -- Yemen's neighbors in the coalition -- have so far paid only a modest proportion of what they promised," he said.

Fighting between the Iran-backed Huthis and government forces aided by the Saudi-led coalition has killed tens of thousands of people, many of whom are civilians, aid agencies say.

The conflict has also forced some 3.3 million people from their homes.