For its part, Iran long has denied supplying any arms to Yemen, though it has backed the Houthis and highlighted the high civilian casualties from the Saudi-led coalition's campaign of airstrikes.
The Saudi-led military coalition fighting Yemen's Shiite rebels bombed the airport in the rebel-held capital, Sanaa, on Tuesday, Yemeni officials said, though there were conflicting reports as to the extent of the damage.
The UN's World Food Programme warned that current stocks of rice will run out in 111 days and wheat in 97.
On Monday, Saudi diplomats announced that the restrictions would be lifted partially, with air and sea ports in areas under government control reopening.
The civil aviation department of Yemen said on Tuesday that the Saudi-led Arab coalition fighting rebels in Yemen inflicted an airstrike on the Sanaa global airport, which resulted in the destruction of its navigation system.
It said Monday the coalition would lift the blockade after widespread global criticism.
The closure of rebel-held ports was "making an already catastrophic situation far worse", they added.More news: Christopher Plummer to replace Kevin Spacey in completed J. Paul Getty biopic
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However other ports, including Houthi-controlled Hodeidah - where some 80 percent of Yemen's food supplies enter - will remain closed until a United Nations verification regime is reviewed to ensure no weapons reach the Houthis, the statement said.
The United Nations has listed Yemen as the world's number one humanitarian crisis, with 17 million people in need of food, seven million of whom are at risk of starvation.
Earlier, the heads of three United Nations agencies warned that without deliveries of vital supplies such as food and medicine "untold thousands of innocent victims, among them many children, will die".
"The supplies, which include medicines, vaccines and food, are essential to staving off disease and starvation". It says over 50,000 children are believed to have died in 2017.
More than 8,670 people - 60% of them civilians - have also been killed and 49,960 injured in fighting on the ground and air strikes since the coalition intervened in the war in March 2015, according to the UN.
For years, war has raged between the Yemen's internationally recognized government and the Houthi rebels who seized Yemen's capital along with the country's northwestern region.
"To deprive this many from the basic means of survival is an unconscionable act and a violation of humanitarian principles and law", the agency directors warned.