Hodeida port has been held by the Iran-backed Huthis since 2014, when the rebels drove the government out of the capital and seized control of territory across northern Yemen and the Red Sea coastline.
On June 13, the UAE, Saudi Arabia and their allies in a pro-government regional coalition launched a major offensive to retake the port, through which nearly three quarters of Yemen's imports flow.
The coalition alleges the port has been used by the rebels as an entry point for weapons smuggled from Saudi Arabia's arch-foe Iran.
On Tuesday, medical sources and residents said an air strike killed eight people travelling on a bus on the road to Zabid in southern Hodeida province.
Their identities could not immediately be confirmed.
A second strike outside Hodeida killed six Huthi rebels travelling in a military vehicle, according to the same sources.
Saudi-led coalition claims killing eight Hezbollah fighters in Yemen
The Saudi-led coalition, which usually conducts air raids in the area, could not immediately be reached for comment.
Exchanges of artillery fire south of Hodeida city also left 38 Huthi fighters and three pro-government troops dead in the past 24 hours, according to medical and local sources.
The UN envoy for Yemen, Martin Griffiths, is due in Yemen's southern city of Aden on Wednesday for talks with President Abedrabbo Mansour Hadi, whose forces have battled for weeks to regain control of Hodeida.
The rebels have said they may be willing to share control of Hodeida's port with the United Nations but say their forces must remain in the docks and the rest of the Red Sea city.
The United Arab Emirates, which has US-trained troops deployed on the ground in western Yemen, is demanding the rebels withdraw from both the port and city to avoid a military assault on densely-populated Hodeida.
"We are hopeful and we believe in the political process," Reem al-Hashimi, the UAE minister of state for international cooperation, said on Tuesday.
Saudi-led coalition captures large areas of Yemen's Hodeidah airport: UAE
But "we cannot imagine a setup where the Huthis can be in the city" of Hodeida, she told reporters in Abu Dhabi.
Griffiths, who held a first round of meetings on the Hodeida crisis in rebel-held Sanaa earlier this month, is holding talks with both sides to "return rapidly to the negotiating table", his office said.
Nearly 10,000 people have died in the Yemen war since 2015 when Saudi Arabia and its allies joined the government's fight against the Huthis.
The conflict has pushed Yemen, long the most impoverished country in the Arab world, to the brink of famine.
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