Hudaida lies some 230km away from the capital, Sanaa, which is controlled by the Houthis.
Almost 10,000 people have been killed since the alliance launched its intervention in Yemen in March 2015, contributing to what the United Nations has called the world's worst humanitarian crisis.
Workers inspect damage at the site of an air strike on the maintenance hub at the Hodeida port, Yemen May 27, 2018. "I hope that it will be possible to avoid a battle for Hodeidah".
"For now yes we can [assist people]", Mohamed Abdi, NRC country director for Yemen, told The Defense Post.
Previous UN efforts have failed to end the war.
The UN pulled all of its worldwide staff out of Al Hodeidah early on Monday morning.
Houthi rebels in Yemen have ramped up missile attacks on Saudi Arabia in recent weeks and months.
The United States warned Monday that aid must flow through the Yemeni port of Hodeida amid reports that Emirati forces plan to seize it from Huthi rebels.
Pompeo's statement, while cautionary, did not explicitly urge the Emiratis to avoid an assault on Hodeidah. Some 600,000 people live in and around the city. He is due to brief the U.N. Security Council later this month.
During the closed session, Griffiths was to brief council members by video-conference from Amman along with United Nations aid chief Mark Lowcock.
"We expect all parties to honor their commitments to work with the UN Office of the Special Envoy of the Secretary General for Yemen on this issue, support a political process to resolve this conflict, ensure humanitarian access to the Yemeni people, and map a stable political future for Yemen". United Nations staff operating out of the port ae already being withdrawn, anticipating the calamity to come.
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