At least 36 Houthi rebels were killed and 50 others injured in the clashes between Yemeni government forces and Houthi rebels on Sunday.
The clashes erupted in al-Malagim district in central al-Bayda province and no information was given as to the loss of army forces, the Yemeni military said in a statement posted on Facebook.
Al-Bayda province has been witnessing gun battles between army units and Houthis over the last few months.
Clashes between government forces and the rebels began weeks ago as government troops have been attempting to advance to the city center from many fronts.
In the city of Midi in Yemen's northwestern Hajjah province, government forces detonated 5,151 mines and explosives planted by a Saudi-led military coalition in the last three months.
Impoverished Yemen has remained wracked by violence since 2014, when Shia Houthi rebels overran much of the country, including the capital, Sanaa.
The conflict escalated in 2015 when Saudi Arabia and its Sunni-Arab allies launched a massive air campaign in Yemen aimed at rolling back Houthi gains.
The violence has devastated Yemen's infrastructure, including health and sanitation systems, prompting the UN to describe the situation as "one of the worst humanitarian disasters of modern times".
