Yemeni forces backed by a Saudi-led coalition launched an assault on Wednesday to retake the port city of Hodeida, which has been controlled by the Iran-backed Huthi rebels along with the capital Sanaa since 2014.
It described the streets of the city as "nearly empty".
For the last few weeks, the United Nations had been trying to broker a deal in a bid to avert the attack, which it fears would further hinder Yemenis' access to food, fuel and medicine - worsening the world's most urgent humanitarian crisis.
The Huthis suffered 30 fatalities on Thursday in clashes near Hodeida airport south of the city, medical sources told AFP. He said it would take Arab forces about 72 hours to clear mines from Hodeidah's port or airport once it captures them. About a quarter of a million people are in danger of injury or death in an urban assault, the United Nations said.
"Four government soldiers were killed in the fighting while more than 10 others were injured", a military source, who preferred not to be named, told Anadolu Agency. "Its goal would be to facilitate the safe transport of humanitarian aid to the population of the city", it said.
Capturing Hudaida would give the Saudi-led coalition the upper hand in the war, in which neither side has made much progress since the coalition intervened in 2015 to restore the internationally recognised government in exile.
Dozens of missiles have been fired at Saudi Arabia in recent months.
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The air attacks targeting Houthi positions have been supported by ground operations by foreign and Yemeni troops south of the Red Sea port. The port of Hodeida is a vital gateway to getting food and other aid to a significant number of these people.
Hodeida, home of almost 700,000 people, is some 150 kilometres (90 miles) southwest of Sanaa, Yemen's capital, which is under Houthi control.
The war in Yemen has displaced 2 million more and helped spawn a cholera epidemic.
About 600,000 people live in and around Hudaida, and "as many as 250,000 people may lose everything - even their lives" in the assault, the United Nations has warned. "With the little money they do have, they buy cooking oil in plastic bags - just enough to cook 1 meal a day", the group said, citing the accounts of staffers. "We have to keep that port open, we have to make sure that people get the supplies that they need".
Marine Maj. Adrian Rankine Galloway, a Pentagon spokesman, said the USA has continued to provide aerial refueling for coalition aircraft and intelligence assistance. That aid including information on key civilian sites that should be not be targeted in strikes in order to avoid civilian casualties.
The Huthis earlier said they had struck a coalition ship off the coast of Hodeida with two missiles.
State-run Saba news agency said the aim of Hadi's first public visit to the country in more than a year was to "supervise" the military operations in Hodeida province.
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"We are at the edges of the airport and are working to secure it now", the Arab coalition said in a statement to Reuters. Two local anti-Houthi Yemeni military officials confirmed the seizure.
The officials spoke on condition of anonymity because they were not authorized to brief media and the witnesses for fear of reprisals.
Houthi leader Abdel Malek Al-Houthi urged troops to "confront the forces of tyranny", warning they would recapture areas taken by pro-government forces by "bringing huge numbers (of fighters) to the battle", according to the rebels' Al-Masirah TV.
"Any closure of the port, even for a few days, will have a dramatic impact on the humanitarian operations in the country", the U.N. Humanitarian Coordinator for Yemen, Lise Grande, told The Associated Press Thursday.
"The coalition and Houthi forces, now fighting for Hodeida, have atrocious records abiding by the laws of war", said HRW's Sarah Leah Whitson.
Mr Al Mouallimi said two ships from Saudi Arabia and the UAE, each carrying 5,000 tonnes of food, were waiting to dock at Hodeidah as part of the coalition's effort to ensure "abundant humanitarian supplies" to the city during the military offensive.
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