The rebels obtain supplies from outside the country through Hodeidah.
Worldwide aid agencies and the United Nations have warned the assault could shut down the vital aid route for some 70 percent of Yemen's food, as well as the bulk of humanitarian aid and fuel supplies.
The attack on Hodeida, however, could derail that effort.
Hodeidah, Yemen's biggest port and the only port controlled by the Houthis, serves as the lifeline for the majority of Yemen's population, which lives in Houthi-ruled territory.
"Without fuel, critical for water pumping, people's access to drinking water will shrink further, leading to even more cases of acute watery diarrhoea and cholera, both of which can be deadly for small children", she added.
"Such hostile acts by the Iran-backed Houthi militias prove the continuing involvement of the Iranian regime in supporting the Houthi militias with qualitative capabilities in a flagrant and explicit violation of the two United Nations resolutions No. 2216 and 2231 with the objective of threatening the security of the Kingdom of Saudi Arabia as well as the regional and worldwide stability".
He said that if the port were to close for any period of time, or "not to operate effectively, the consequences in humanitarian terms would be catastrophic".
On Thursday, coalition troops took the town of Nakhila in Yemen's ad-Durayhimi district, some 20 kilometers (12 miles) south of Hodeida International Airport, according to Yemen's government-run SABA news agency.
Sources in the Saudi-led coalition said the alliance had carried out 18 air strikes on Huthi positions on the outskirts of Hodeida in recent hours.
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Early on Wednesday, convoys of vehicles headed towards the rebel-held city as heavy gunfire rang out.
The initial battle plan appeared to involve a pincer movement. About 2,000 troops who crossed the Red Sea from an Emirati naval base in the African nation of Eritrea were awaiting orders to move in from the west after Yemeni government forces seize Hodeida's port, Yemeni security officials said.
Russia's U.N. Ambassador Vassily Nebenzia, the current council president, told reporters Wednesday that the United Kingdom asked for the meeting.
The officials and residents spoke on condition of anonymity because they were not authorized to brief the media and for fear of reprisals.
The Huthis captured Hodeida and Yemen's capital Sanaa in 2014.
Four Emirati soldiers were killed in Wednesday's assault, the United Arab Emirates' state-run news agency said, but gave no details of how they died.
The war pits the Houthis against the Western-backed Sunni Muslim states, which intervened in 2015 to restore the exiled government and thwart what Riyadh and Abu Dhabi see as expansionist aims Iran.
The UN on Monday withdrew all of its worldwide staff from Hodeida ahead of the impending assault, warning that any offensive would put millions of lives at risk.