Saudi-led coalition warplanes and Apache helicopters provided "continuous" air support to ground forces, striking Houthi positions, military sources said on Thursday.
Tribal fighters loyal to the Yemeni government stand by a tank in Al Faza area near Hudaida earlier this month.
Civil war has raged in Yemen since late 2014, when the Houthis and allied forces seized north-western parts of the country, including the capital Sanaa, and eventually forced President Abdrabbuh Mansour Hadi to flee overseas.
According to the Houthis, a pair of missiles struck a landing ship as it was conveying equipment and personnel ashore, leading to the retreat of a flotilla of coalition vessels and a search and rescue operation.
"Today I heard warplanes hovering and the sounds of explosions", a 20-year-old woman, who wished to remain anonymous for fear of reprisal, told Al Jazeera.
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Saudi Arabia and the UAE say they have plans in place to prevent the battle from causing a humanitarian disaster.
Field commanders said that troops pushed towards Hodeida airport after Yemeni pro-government forces received a "green light" from the coalition.
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Yemen's exiled government said in a statement that it "has exhausted all peaceful and political means to remove the Houthi militia from the port of Hodeida", according to The Associated Press. "Liberation of the port of Hodeida is a milestone in our struggle to regain Yemen from the militias".
Human rights groups say airstrikes carried out by the Saudi-led coalition have killed and wounded thousands of civilians, often in indiscriminate attacks. The port is some 150 kilometres southwest of Sanaa, Yemen's capital, which has been in Houthi hands since September 2014.
Its leader, exiled President Abd-Rabbu Mansour al-Hadi, said his government had proposed compromises but would not let the Houthis hold the Yemeni people "hostage to a prolonged war which the Houthis ignited".
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"Hodeidah is absolutely essential to the preserving of life", the United Nation's emergency relief coordinator, Mark Lowcock, said this week.
"Hodeidah is a lifeline for millions and millions of Yemenis", Iolanda Jaquemet, a spokeswoman from the International Committee of the Red Cross (ICRC), told RT.
Foreign Secretary Boris Johnson said on Wednesday the British government was in contact with the alliance about ensuring its operations comply with global law on protecting civilians. A Saudi-led airstrike in 2015 destroyed cranes at Hodeida.
Coalition spokesman Turki al-Malki has said operation "Golden Victory" aimed to wrest control of the port and airport, but that they would avoid entering the city, where the Houthis have deployed military vehicles and troops. Yemen is heavily dependent on imported food, fuel and medicine that come through Hodeidah port. The United Nations in January shipped in mobile cranes to help unload ships there.
It estimates 600,000 people live in the area, and in a worst-case scenario a battle could cost up to 250,000 lives, as well as cutting off millions from aid and supplies.
We will update this article when more information becomes available.
Jolien Veldwijk, the acting country director for CARE International, called the attack "catastrophic, hopeless and devastating".
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