A Friday night air strike hit a Houthi military vehicle passing through the province's Maqbanah district, killing four civilians and five fighters.
A Saudi coalition air strike in the battleground Yemeni province of Taiz has killed five Houthi fighters and four civilians.
The Friday night strike targeted a Houthi military vehicle as it was passing through Maqbanah district, about 35 kilometres (22 miles) northwest of Yemen's third largest city Taiz.
"The Houthi military vehicle was passing down a road and four civilians got in before it was struck by coalition jets, resulting in all nine deaths," a local official said on Saturday, speaking on condition of anonymity.
A medical source confirmed the death toll and added that two civilians were also wounded.
Houthi-controlled media, on the other hand, said that 18 civilians had been killed. There was no immediate comment from the coalition.
Taiz remains under the control of the Saudi-backed government but most surrounding districts, including Maqbanah, are held by the rebels, leaving its population of around 600,000 dependent on a single supply route.
The Saudi-led coalition has been fighting alongside government forces since 2015, a year after the Houthis overran the capital Sanaa.
A UN report last week said 377,000 people will have died by the end of 2021 through direct and indirect impacts of the Yemen war.
Millions of people have been displaced by the fighting and more than 80 percent of the population require some form of assistance in what the United Nations has described as the world's worst humanitarian crisis.