Before the war, more than 70 per cent of Yemen's food and fuel imports came through Hodeida, accounting for more than 40 per cent of the nation's customs income.
Saudi-owned satellite news channels and later state media announced the battle had begun, citing military sources.
The Saudi-Emirati coalition's initial battle plan appears to involve a pincer movement.
The fighting Wednesday led to the closure of Hudaida's Red Sea port, which will affect food and medicine deliveries to Yemen.
The Emirati news agency Wamsaid attacking forces had managed to "liberate areas.in the surroundings of the airport" and captured or killed "dozens" of Iranian-backed Houthis.
The United States rejected a request from the UAE for intelligence, mine-sweeping and airborne intelligence, surveillance and reconnaissance (ISR) assets for the Hodeidah operation, a UAE official said, speaking on condition of anonymity, while noting congressional opposition.
"The liberation of Hodeidah port is a turning point in our struggle to recapture Yemen from the militias that hijacked it to serve foreign agendas", the exiled government said in a statement carried by state-run Yemeni media.
A Houthi statement warned commercial ships in the Red Sea, one of the world's most important trade routes, to stay 20 miles from coalition warships or potentially face attack. "An essential lifeline that was previously plagued by the Iranian backed Houthi militia", he added. The Saudi-led coalition entered the war in March 2015.
Yemen's internationally recognized government earlier said negotiations had failed to force the rebels from Hodeida, and a grace period for UN-led peace efforts was over.
The assault began after the expiry of a deadline set by the United Arab Emirates for the Houthis, who hold the capital Sanaa, to hand over the sole port under their control.
Capturing Hodeidah would give the coalition a major boost in the war.
Recent CDC report finds rates increasing
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The United Nations and other aid groups already had pulled their global staff from Hodeida ahead of the rumored assault.
The port remained open, however. Several ships have arrived in recent days, including oil tankers, and there has been no word from the coalition or United Nations to stop work, according to a senior port official, who spoke on condition of anonymity because he was not authorized to talk to the press. The two countries also said they would operate a dedicated shipping lane to Hodeida from Abu Dhabi and the southern Saudi city of Jizan to deliver food and medical supplies.
The population may find itself "on the brink of death" if the fighting leads to a blockade of the port, it said.
The UN Children's Fund (UNICEF) has raised alarm over the plight of Hodeida's 300,000 children and the risk that drinking water supplies will be disrupted.
More than 10,000 people have died and 3 million displaced in that time.
"Equally vital is that the Saudi Arabia-led coalition and Huthi forces ensure the flow of aid and essential goods isn't impeded in any way, as millions of people remain at risk of starvation across the country".
He said "aid operations will be severely challenged in the event of sustained fighting in densely populated urban areas" and stressed that people trying to flee conflict areas "must be allowed to do so without any hindrance".
"We hear sounds of explosions. We are gravely concerned that parts of the population could experience starvation".
Humanitarian organisations had developed "contingency plans" for the event of an attack affecting the 600,000 people living in and around Hodeida, she said.
Aid workers had similar worries.
Jolien Veldwijk, acting country director for the charity CARE International called the attack "catastrophic, hopeless and devastating", worsening hunger as food will become harder to find and more expensive.
On Monday Spain stepped in and announced that the ship would be allowed to dock in the southeastern city of Valencia. Spain's new Socialist Prime Minister Pedro Sanchez agreed to allow the ship to dock in its eastern port of Valencia.
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