The statement on the government-controlled SABA news agency called the battle for Hodeida"a milestone in our struggle to get Yemen back from the militias."
Exiled President Abed Rabbo Mansour Hadi and many of his advisers now live in Saudi Arabia after Shiite rebels known as Houthis seized Sanaa in September 2014. A Saudi-led coalition entered the conflict in March 2015. Hadi earlier travelled to the UAE on Tuesday to discuss the assault.
"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 separate statement carried by state-run Yemeni media.
"The liberation of the port is the start of the fall of the Houthi militia and will secure marine shipping in Bab al-Mandab strait and cut off the hands of Iran,which has long drowned Yemen in weapons that shed precious Yemeni blood."
The assault is the first time since the Western-backed coalition of mostly Gulf states joined the war in 2015,that they have attempted to capture such a well-defended major city,with the aim of boxing in the Houthis in Sanaa and cutting their supply lines to force them to the negotiating table.
The alliance intervened in Yemen to restore Hadi's government and thwart what Riyadh and Abu Dhabi see as the expansionist aims of their Shiite foe,Iran.
The Houthis did not immediately acknowledge the start of the battle.
Forces loyal to Yemen's exiled government and irregular fighters led by Emirati troops had neared Hodeida in recent days. The port is some 150 kilometres south-west of Sanaa.
Emirati Minister of State for Foreign Affairs Anwar Gargash earlier told French newspaperLe Figaro the deadline for a withdrawal from Hodeida by the Houthis had expired early Wednesday morning.
More than 10,000 people have been killed in Yemen's civil war. The Saudi-led coalition has been criticised for its air strikes killing civilians.
The Houthis deny they are Iranian pawns and say their revolt aims to target corruption and defend Yemen from invaders.
The United Nations had been trying in the last few weeks to get the parties to reach a deal that would avert the attack,which it fears would further impede Yemenis'access to food,fuel and medicine,exacerbating the world's most urgent humanitarian crisis in the impoverished Arab state.
The UAE has said coalition forces plan to keep the port operational but warned the Houthis could sabotage infrastructure and place land and sea mines as they withdrew.
Reem al-Hashimy,the UAE minister of state for international cooperation,has said if the port was wrested from the Houthis,the coalition could ease controls aimed at denying the group arms and ease the flow of goods and aid into the co7untry to avert face starvation and disease.
The Emirates say the Houthis use the port to smuggle Iranian-made weapons,including missiles that have targeted Saudi cities - accusations denied by the group and Tehran.
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The UN says some 600,000 people live in and around Hodeida,and"as many as 250,000 people may lose everything- even their lives"in the assault.
"As has been the case since the beginning of the war,the cost of the battle for Hodeida will largely accrue to the already impoverished civilian population,"the International Crisis Group warned in a report Monday.
The US has provided the Arab coalition with logistical support,but it's unclear what position the Americans will take on a full-scale attack on Hodeida.
US Secretary of State Mike Pompeo said he had spoken with Emirati officials and"made clear our desire to address their security concerns while preserving the free flow of humanitarian aid and life-saving commercial imports."
Analysts warned that while the Houthis may not need the customs money,they likely want to bleed the coalition with mines and guerrilla fighting.