The fighting flared when forces loyal to President Abedrabbo Mansour Hadi attacked rebels in Bayhan district, on the border between Shabwa and Marib provinces.
Bayhan is the only part of Shabwa province still controlled by the Iran-backed rebels after government forces supported by the Saudi-led Arab coalition last year expelled them from five southern provinces.
"The death toll of the Huthis has reached 28 while 12 soldiers of the legitimate forces were killed," a military official said.
The Yemen conflict has killed some 7,000 people since the Saudi-led intervention in March 2015, according to the United Nations.
The coalition began the military campaign against the rebels after they closed in on Hadi in his refuge in the southern city of Aden, forcing him to flee to Riyadh.
The rebels and allied renegade troops loyal to former president Ali Abdullah Saleh continue to control the capital Sanaa, which they overran in September 2014, along with several mainly northern regions.
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