Fierce battles erupted in the northern Jawf province when Huthi rebels attacked loyalists in al-Motoon district, triggering a counter attack by government forces backed by warplanes from the Saudi-led coalition, a military official said.
The fighting left 13 rebels dead, while eight loyalists were killed by mistake in an air strike that missed its target, the official added.
Further south, three Huthi rebels were killed in clashes in Bayhan, Shabwa province, another 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.
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Those talks received a new blow yesterday when government representatives demanded a full withdrawal of Iran-backed rebels from territory seized since 2014.
On Wednesday, the rebel delegation said it would not sign up to any deal on military and security issues until there was agreement on a consensus president and a national unity government to oversee the transition.
Despite a 15-month Saudi-led military intervention in support of the government of President Abedrabbo Mansour Hadi, the rebels and their allies remain in control of swathes of territory they have overran since 2014, including the capital Sanaa.
More than 6,400 people have been killed since the intervention began, the majority of them civilians, and there has been growing international pressure for an end to the conflict.