The fighting late Monday north of Taez, held by loyalists but partly surrounded by Shiite Houthis and their rebel allies, left at least 14 rebels and eight soldiers dead, they said.
Residents said relative calm was restored on Tuesday.
In the north, two loyalist officers were killed in clashes around the Red Sea port town of Midi, the sources said, while a rights activist said a 13-year-old girl died when a shell fired by rebels crashed into her home in the southern province of Dhaleh.
Yemen's 20-month-old conflict has killed more than 7,000 people and wounded nearly 37,000, the United Nations says.
The Houthis overran the capital Sanaa and other parts of the impoverished country in September 2014, prompting a Saudi-led Arab military coalition to intervene six months later in support of President Abedrabbo Mansour Hadi.