Saudi placed the current blockade on Yemen a week ago, after Houthi rebels fired a missile at Riyadh.
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.
Earlier this month, the Saudi-led coalition closed access to Yemeni ports following a ballistic missile attack toward Riyadh by Houthi rebels.
Noting that there were three weeks of vaccines left in the country, McGoldrick said "humanitarian supplies are dangerously low".
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A statement issued by the Coalition on Monday said it hopes the United Nations teams of experts would prevent "the smuggling of weapons, ammunitions, missile parts and cash that are regularly being supplied by Iran and Iranian accomplices to the Houthi rebels".
Yemeni officials say the Saudi-led coalition has bombed the airport in the rebel-held capital, Sanaa, damaging the runway and a ground navigation tower. While the language of the resolution calls to "increase efforts to adopt all necessary and appropriate measures to prevent civilian casualties and increase humanitarian access", it does not call for an end to US support of the Saudi-led coaltion attacking Yemen.
Last week, the World Health Organization warned that more Yemeni civilians will die over the closure of the Yemeni ports. The Houthis control most of northern Yemen.
The conflict escalated when Saudi Arabia and its Arab allies launched a massive air campaign in 2015 aimed at reversing Houthi military gains and strengthening Yemen's embattled government.