Yemen's pro-government forces backed by the Arab coalition recaptured the Red Sea mill and other factories on Tuesday as the Al Amalikah brigades advanced closer to rebel-held Hodeidah.
The retaking of the mill, east of Hodeidah, from Houthi fighters marks a significant victory for the Yemeni military as it means taking control of one of the rebel group's food supplies.
One Hodeidah resident told The National that Houthi fighters had shelled factories on Wednesday killing four workers and injuring more than eight. .
In September UN humanitarian coordinator Lise Grande said in a statement that the Red Sea mill had 45,000 metric tonnes of food inside. "Enough to feed 3.5 million people for a month," she said. "If the mills are damaged or disrupted, the human cost will be incalculable."
The spokesman for the Al Amalikah brigades Colonel Mamoon Al Mahjami told The National that pro-Yemeni forces had been advancing steadily toward Hodeidah in a bid to create a noose around the city of 600,000 and force rebel fighters to surrender.
"The ultimate goal is to impose a strict siege around the Houthi fighters who are still stationed amid the populated neighbourhoods in the city center," he said.
A medical source said on Wednesday that the Houthis had forced medical staff out of the May 22 hospital - one of Hodeidah's main medical facilities - and stationed snipers on top of the building.
In the past 24 hours fighting claimed the lives of 27 rebels and 12 pro-government fighters on the outskirts of Hodeidah city, a medical source told Agence France-Presse on Wednesday.
The clashes come as the United Nations pushes to restart negotiations between the warring parties, after planned talks in Geneva in September failed.