"We have taken control of the main southeast entrance and will move forward," said Colonel Adnan Almateri, the chief of joint operations in the area.
A senior Houthi political official disputed this, saying rebel forces still controlled the main southern entrance to Hodeida and had used roadside bombs and other means to stop their enemies.
"The coalition wants to take over the city and use that as a playing card to apply economic pressure on the Yemeni people and make them starve and therefore give in to the coalition," said Dhaifallah Alshami, the Houthi official.
"However, that will never happen. The will of the Yemeni people cannot be broken."
Inside Hodeida, residents reached by telephone said they were living in apprehension.
"We have been hearing heavy and midsize machine gun firing, mortar shelling and airstrikes in the outskirts of the city, near the entrance of the city, especially at night for the past few days," said Mazen Mujammal, 21. "There is a great sense of panic and fear among people."
He and other residents said that the city was suffering shortages of food and medicine and that the rebels were patrolling the streets. Most shops and restaurants have closed. It was difficult for most residents to flee because of the ongoing clashes near the entrance to the city.
"The shootings and bombings are outside the city, in the southern part," said Majed Qadoo, 35, a government employee. "Inside the city, the situation is stable. People fear, however, that the bombings and shootings will reach them inside the city."
Almateri, the coalition commander, vowed that coalition troops would march into Hodeida.
"There will be no dialogue with the enemy or stopping before liberating the country from them. They do not seek peace and are nothing but a destruction tool," Almateri said.