Troops killed the rebel fighters on Saturday as they attempted to reopen key routes in Saada province on the Saudi border, the official Saba news agency quoted the commander as saying without giving his name.
The rebels have set up roadblocks and planted mines on a number of roads in the province.
In neighbouring Jawf province, troops captured three rebels, a security official said.
On Thursday, the army said it had made major advances in Amran province which lies between Saada and the capital Sanaa. On Friday, it said it was intensifying its operation to reopen the key link that passes through the province.
The Sanaa government launched operation “Scorched Earth” on August 11 in a bid to crush the Shia rebellion which first erupted in 2004.
Published by Mike Hitchen i On Global Trends, world news, analysis, opinion
Putting principles before profits
Yemen
Putting principles before profits
Yemen