Rights groups have accused the Saudi-led coalition fighting Yemen's Shiite rebels of bombing civilian gatherings, markets, hospitals, and residential areas across Yemen.
"We call on all parties to end this devastating conflict", the two United Nations organizations said in their statement.
Earlier, the officials said the family was fleeing from the fighting raging in the province.
Unusually in Yemen's fractured political landscape, Islah has supporters in the north and south of the country.Since the Saudi-led coalition intervened in Yemen in 2015, Islah has tried to distance itself from the Brotherhood, in deference to the government-in-exile's Saudi hosts.
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Lok Sabha Speaker Sumitra Mahajan on Sunday said all parties have assured that the monsoon session will proceed without any ruckus or uproar.
The UNHCR has said that this attack "demonstrates the extreme danger facing civilians in Yemen, particularly those attempting to flee violence".
The civilians killed in the attack were refugees fleeing embattled Mawza district in Taiz governorate aboard a packed vehicle and were understood to be from the same family, UNHCR said.
Save the Children has warned that if the United Nations fails to include Saudi-led coalition on this year's list, it will set a unsafe precedent for other conflicts around the world.
More than half a million people have been forced to leave their homes in the Taiz region, representing more than a quarter of all internally displaced people in Yemen. Their goal is to drive rebels out of Yemen's coastline. "UNHCR, as the lead agency for protection under the coordinated humanitarian response in Yemen, has been appealing to parties to the conflict to ensure their utmost in the protection of civilians and the mitigation of suffering".
Impoverished Yemen has remained in a state of civil war since 2014, when Houthi rebels overran much of the country, including Sanaa.
Saudi Arabia is using British-manufactured weapons in the offensive, sparking failed legal challenge by the Campaign Against the Arms Trade in the High Court.