"We are now destroying Houthi fortifications near the airport," spokesman Turki al-Malki said in an interview with Al Arabiya television from Brussels, accusing the Houthis of placing tanks inside residential areas.
Residents said clashes at the airport have abated but coalition warplanes were bombing positions held by the Iran-aligned Houthis as the group dug in to defend Hodeidah, its sole port and the lifeline for millions of Yemenis.
Coalition leaders Saudi Arabia and the United Arab Emirates have pledged a swift assault aimed at taking control of the strategic Red Sea city and port, to avoid disrupting aid deliveries to impoverished Yemen.
"Hodeidah port is operating as normal and the movement of ships is normal," Malki said. "We have humanitarian and development plans for when we liberate the city."
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The United Nations fears the offensive will worsen what is already the world's most urgent humanitarian crisis, with 22 million Yemenis dependent on aid and an estimated 8.4 million believed to be on the verge of starvation.
The escalation in fighting has wounded and displaced civilians and hampered humanitarian agencies.
The Arab states say their aim is to seize the airport and port quickly and avoid street battles in the city centre. But the Houthis were well dug into Hodeidah as it constitutes the key supply line to territory they control, including the capital, Sanaa.
The coalition intervened in Yemen's war in 2015 to try to unseat the Houthis, restore the internationally recognised Yemeni government in exile and thwart what Riyadh and Abu Dhabi see as Iran's expansionism in the region.
The Houthis, who control the most populated regions in the chronically unstable nation of 30 million people, deny they are puppets of Iran. They say their movement reflects a popular revolt against state corruption and foreign meddling.