Houthi rebels are stopping residents of Al Duraihimi, a district south of the Red Sea port city of Hodeidah, from leaving before an offensive by pro-government troops.
The rebels have been using military vehicles to block routes out of the city, residents told The National on Monday, and some are demanding ransom from civilians to allow safe passage.
Zakaria Al Kurashi, from Al Duraihimi, said pro-government forces had been using loudhailers to announce an advance towards Hodeidah, urging people to leave.
But the Houthis then sealed off routes out of villages.
"We tried to flee out of the area but the Houthis refused to let us go. They have been trying to blackmail us. If you want to take your family out of the clashes area you must pay 100,000 Yemen rials [$400]," he said.
Sources said coalition forces were stationed near the centre of Al Duraihimi.
Conditions for residents are poor.
"We are suffering very much, with no water, no gas, our children are starving, and we keep struggling most of the day to bring a 20 litre bottle of water to drink because the rebels pounded the only water storage that was feeding the villages in the north of Al Duraihimi," Mr Al Kurashi said.
Fighting in Hodeidah province has killed dozens of rebels and pro-government forces in recent days, with Yemeni officials and witnesses putting the toll at 80.
The Yemen government of President Abdrabu Mansur Hadi last week called for more political pressure to be applied on Houthi rebels before peace talks being convened by the UN special envoy next month.
Ahmed Awad bin Mubarak, Yemen's permanent representative to the UN, told the Security Council on Thursday that more was needed to stop the Houthis launching attacks on international shipping.
He cited the rebels' attacks last week on two Saudi oil tankers in the Red Sea as examples, as well as the laying of hundreds of seamines targeting Yemeni ships and fishermen.
The Saudi-led Arab Coalition supporting the Yemeni government said those attacks were launched from Hodeidah.
The UN special envoy for Yemen, Martin Griffiths, had urged the council to do more to “keep the Red Sea out of the conflict” as he unveiled plans to begin a first round of peace negotiations in Geneva on September 6.
A coalition-led offensive to retake Hodeidah was suspended early last month to assist mediation efforts by Mr Griffiths.
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