The United Nations has warned a total blockade could cause starvation in Yemen, where war has killed at least 10,000 people in the last two and a half years.
Meanwhile in the Yemeni capital, Sanaa, the United Nations dismissed Houthi claims that a Saudi-led air strike had destroyed the navigation station of the global airport, which is critical to receiving already limited aid shipments.
Saudi Arabia and its allies intervened in Yemen in March 2015 to push back the Houthi rebels who control the capital Sanaa, and restore the government of President Abedrabbo Mansour Hadi to power.
He says they are now inaccessible to United Nations aid shipments.
Jamie McGoldrick of the UN Office for the Co-ordination of Humanitarian Affairs, who is based in Amman, said UN staff had visited the airport and spoken with authorities there.
The U.S. House of Representatives overwhelmingly voted for a resolution declaring that U.S. military assistance to Saudi Arabia in its war in Yemen is not authorized under previous legislation which has given the president power to combat terror overseas and invade Iraq in 2003.
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"The humanitarian impact of what is happening here right now is unimaginable", he told reporters in Geneva in a phone conference. The Saudi-led coalition has said it will keep Hodeidah port closed until a United Nations verification programme is reviewed to ensure no weapons reach the Houthis.
The Saudi-led coalition hopes that will prevent "the smuggling of weapons, ammunitions, missile parts and cash that are regularly being supplied by Iran and Iranian accomplices to the Houthi rebels", the statement said.
However, Mr McGoldrick said there was "no indication" yet of the blockade being lifted.
Saudi Arabia and the USA have accused Iran of supplying the ballistic missile used in that attack.
Al-Mouallimi told reports from NY that the Coalition would conduct this process in complete agreement with Yemen's internationally recognized government, to allow the safe delivery of humanitarian aid. However, Saudi Arabia demanded more rigorous checks at the Red Sea port of Hodeida, which is being controlled by the rebels.
Those ports are in Yemeni cities of Aden, Mocha and Mukalla. And landing aid there would also involve having to cross front lines to deliver it.