At the airport, which the coalition has controlled since Saturday, their forces stormed the main compound and took full command.
Officials also displayed a series of drones they said showed a growing sophistication by the insurgents, starting first with plastic foam models that could be built by hobby kit to one captured in April that closely resembled an Iranian-made drone.
The Norweigan Refugee Council said on Monday that Houthi fighters were closing all main roads to the city and had completely stopped travel on the main road linking to the capital Sana'a.
The coalition has said it intends to quickly secure the port and then avoid pitched battles in Hodeidah city, where some 600,000 people are estimated to live.
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"I wish we were seeing more from the global community", she told Reuters. "There's a lot they can do and now is the time to do it".
United Nations officials estimate that 600,000 people live in and around Hodeidah and that in a worst-case scenario the battles could cost up to 250,000 lives.
The U.N. World Food Programme said on Tuesday it was hastening to unload three ships at the port that contain enough food for six million people for one month.
"Coalition's aid shipments have frequently been confiscated by militias and found their way to the black market but this has not derailed the coalition commitment to alleviate the humanitarian crisis", he said.
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Colonel al-Malki referred to the process and the political efforts in Yemen, the most recent of which was the visit of UN Special Envoy for Yemen Martin Griffith to Yemen in early June, during which he met with the Yemeni President Abd Rabbo Mansour Hadi and some representatives of the countries of the region, before moving to Sana'a.
A senior Houthi official, Mohammed al-Bukaiti, confirmed the fierce fighting at the Hodeida airport. "The western coast will be a swamp that drowns and finishes the forces of the invaders and the aggressors". "The streets have been turned into a big audio stage to boost their fighters' morale".
It sparked an outcry from relief organisations who warned of the risk of starvation if aid shipments and commercial food imports were not fully restored.
Iran's mission to the United Nations later said it had no comment on the specifics of the Saudi-led coalition's allegations "other than reiterating that Iran has not sent and does not send armaments to Yemen".
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Taking Hodeidah could hand a long sought edge to the Arab alliance which, despite superior weaponry and firepower, has failed to defeat the Houthis in a grinding war that has killed more than 10,000 people. They say their movement reflects a popular revolt against state corruption and foreign meddling.