Engineers worked to clear mines from areas around Hodeida International Airport, just south of the city of some 600,000 people on the Red Sea, the military of Yemen's former government said, AP reported.
Other government officials and witnesses later said coalition forces had not yet fully taken control of the airport. They said fighting was heavy just outside the airport gates.
Sadek Dawad, spokesman of the Republican Guards force loyal to the Saudis, said forces had battled onto the airport grounds.
Dawad also said the southern gate of Hodeida city was captured by pro-coalition forces.
The Houthis, who hold the country's capital of Sana’a, did not immediately acknowledge losing the airport.
The Houthi-run Al-Masirah satellite news channel aired footage it described as being from near Hodeida showing a burned-out truck, corpses of irregular militiamen and a damaged Emirati armored vehicle.
Witnesses said forces from the United Arab Emirates-backed Amaleqa brigades, backed by air cover from the Saudi-led coalition, were heading to eastern Hodeida province to attempt to cut off the main road that links it with the capital, Sana’a.
The Norwegian Refugee Council said humanitarian agencies cannot reach the southern part of Hodeida as fighting escalated. It said in a statement that heavy airstrikes by the Saudi-led coalition have moved confrontations lines deeper in the south.
United Nations special envoy Martin Griffiths, meanwhile arrived in Sana’a in an effort to broker a cease-fire.
The Saudi-led coalition began its assault Wednesday on Hodeida, the main entry for food into a country already on the brink of famine. Emirati forces are leading ground forces mixed with their own troops, irregular militiamen and soldiers backing Yemen's former government. Saudi Arabia has provided air support, with targeting guidance and refueling coming from the US.
International aid groups and the UN cautioned the Saudi-led coalition from launching the assault. Their fear is that a protracted fight could force a shutdown of Hodeida's port at a time when a halt in aid risks tipping millions into starvation. Some 70 percent of Yemen's food enters via the port, as well as the bulk of humanitarian aid and fuel supplies. Around two-thirds of the country's population of 27 million relies on aid and 8.4 million are already at risk of starving.
The coalition has blocked most ports, letting supplies into Hodeida in coordination with the UN. The air campaign and fighting have disrupted other supply lines, causing an economic crisis that makes food too expensive for many to afford.
Aid agencies and the UN evacuated international staff from the city ahead of the offensive. Some of the wounded able to flee are driving onto Aden, some 315 kilometers (195 miles) away, after being stabilized at a hospital in Mocha on the way, the aid group Doctors Without Borders said. The local hospital in Hodeida already is struggling to help the wounded, the group said.
Thousands remain besieged in the city and around the airport due to the fighting.
The Houthis seized control of Sana’a in September 2014, later pushing south toward the port city of Aden. The Saudi-led coalition intervened in March 2015 and has faced criticism for a campaign of airstrikes killing civilians and destroying hospitals and markets.