As many as 29 Houthi militants were killed and injured, while 17 others were captured in military operations launched by fighters loyal to president Abd Rabbu Mansour Hadi.
Nine of the Houthi rebels and forces of ousted president Ali Abdullah Saleh were killed when the pro-Hadi fighters repulsed their attacks northwest of Marib.
One pro-Hadi fighter was killed and three others injured in a Houthi attack, said security sources.
Also, 15 of Houthis and Saleh's troops were killed and injured in an attack in Taiz.
The pro-Hadi fighters, known as the Popular Resistance forces, have been backed by a Saudi-led coalition that launches air strikes to expel Houthi rebels from the capital Sanaa and several provinces.