The announcement from the Saudi mission at the United Nations came after the coalition fighting Yemen's rebels, known as Houthis, faced widespread global criticism over the closure, with the U.N. and over 20 aid groups saying it could bring millions of people closer to "starvation and death".
Save the Children reported that Yemen will see an average of 130 children a day - or one child every 10 minutes - die this year due to obstructions to humanitarian aid and what is now regarded as the largest cholera outbreak seen in modern history.
While welcoming the re-opening of Aden port, the United Nations chief said this alone will not meet the needs of 28 million Yemenis, Dujarric told a daily press briefing.
"The humanitarian impact of what is happening right now is unimaginable", he said. For ports in rebel-held or disputed territories, such as the city of Hodeida, the mission said it has asked the U.N.to send a team of experts to discuss ways to make sure weapons can't be smuggled in.
Saudi Arabia has since said that aid can go through "liberated ports" but not Houthi-controlled Hodeidah, the conduit for the vast bulk of imports into Yemen.
So far, 29 vessels with 300,000 tonnes of food and 192,000 tonnes of fuel had been prevented from reaching Yemen, and a United Nations ship transporting 1,300 tonnes of health, WASH (water, sanitation and hygiene) and nutrition supplies had been unable to dock at Hudaydah, they added.
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"We are concerned that not enough has happened", he said.
More than 20 million people, more than half of whom are children, are in need of urgent assistance. "The humanitarians are just holding things together, waiting for a peace process which is very much in the distance".
The UN's World Food Programme warned that current stocks of rice will run out in 111 days and wheat in 97.
The U.N. children's agency UNICEF had only three weeks of vaccine supplies left in Yemen, and both UNICEF and the World Health Organization had shipments of essential medicines and vaccines blocked in Djibouti, McGoldrick said.
Yemen's national airline said on Tuesday a commercial flight had landed at Aden worldwide airport after acquiring security permits, a step that will ease a blockade on one of the poorest Arab nations.