The deaths came in Bayhan district as troops responded to a rebel offensive yesterday, the sources told AFP.
Bayhan is the sole district of Shabwa still held by the rebels, who control neighbouring Baida province and most of northern Yemen.
Both provinces have also been targeted by a long-running US drone war against Al-Qaeda, which has taken advantage of the conflict between the government and the rebels to consolidate its presence.
Despite the military intervention of a Saudi-led coalition in 2015, the government's authority is still largely confined to the south and areas along the Saudi border.
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