The clashes erupted when Huthi rebels and allied forces loyal to former president Ali Abdullah Saleh attacked government positions in Bayhan district on the border between Shabwa and Marib provinces, said General Misfer al-Harithi, who commands the 19th infantry battalion.
Troops counter-attacked and pushed the rebels back, he said.
"Our forces managed to recapture several positions. The fighting resulted in the death of 25 Huthis and Saleh loyalists and 14 from our forces," Harithi said.
Today's fighting flared despite an early April ceasefire that paved the way for ongoing peace talks in Kuwait.
More than 6,400 people have been killed in Yemen since the coalition began a campaign in March 2015 against the rebels who had occupied the capital and advanced on Hadi's refuge in the south, forcing him to flee to Riyadh.