The Iran-backed Huthi rebels pressed ahead with attempts to advance towards the strategic Al-Anad airbase, in the southern province of Lahj, a military official said.
The rebels and their allies of forces loyal to former president Ali Abdullah Saleh captured the area of Qubaita, on the frontier between Lahj and Taez province.
Eleven rebels were killed when warplanes from the Saudi-led coalition bombed them in Qubaita and Kirsh, the official said.
Six other soldiers were killed in clashes in the flashpoint city of Taez, where rebels attacked an army base, a military official said.
Meanwhile, nine rebels and seven soldiers were killed in the past 24 hours in clashes in northern Yemen, after rebels attacked loyalists in Nahm, northeast of the capital Sanaa, a military official said.
Clashes have continued despite a UN-brokered ceasefire that entered into effect on April 11 and paved the way for peace talks in Kuwait.
The Huthis overran the capital in late 2014 before moving into other parts of Yemen, prompting a Saudi-led coalition to intervene in March last year.
The United Nations says more than 6,400 people have been killed in Yemen since then, mostly civilians.
The fighting has also driven 2.8 million people from their homes and left more than 80 percent of the population in need of humanitarian aid.
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