Yemen already has 7 million people on the brink of starvation, but without the reopening of all ports that number could grow by 3.2 million, the heads of the World Food Programme, UNICEF and the World Health Organization said in a joint statement.
Hedile noted the first flight carrying 218 passengers took off today.
Save the Children said late Wednesday that a continuing blockade by the Saudi-led coalition fighting Yemen's Shiite rebels is likely to increase the death rate.
The coalition said Monday that it would reopen ports in areas held by allied forces and loosen restrictions it had raised after the firing of the missile, which was intercepted near Riyadh's worldwide airport. Aden had been the only such port accepting shipments recently.
Saudi Crown Prince Mohammed bin Salman accused its regional rival Iran of supplying the missile but Iranian President Hassan Rouhani denied arming the Houthis and said the attack was a "reaction" by Yemenis to coalition air strikes.
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Despite the Saudi announcement, a top leader of Yemen's Shiite rebels on Monday vowed retaliation against the oil-rich kingdom over its disastrous blockade of his war-torn country.
Al-Sammad said that with the blockade, the coalition "shut down all doors for peace and dialogue".
In another development, Daesh claimed responsibility for a auto bombing that security sources said killed 10 people, including civilians, at a security post in the government bastion of Aden on Tuesday. The more the blockade tightens, he said, the more the Houthis will develop their abilities to "respond to the assault of the enemy".
The conflict in Yemen began in 2015 and is largely seen as a proxy war between Saudi, who leads a coalition that backs the Yemeni government, and Iran, who backs the Houthi rebel movement. The move came after Saudi Arabia intercepted a missile fired towards Riyadh, which it blamed on Tehran.
The heads of three United Nations agencies urged the Saudi-led military coalition on Thursday to lift its blockade on Yemen, warning that "untold thousands" would die if it stayed in place.