At least four Shia Houthi fighters have been killed in Radaa while battling Al-Qaeda in the Arabian Peninsula.
Houthis are also pushing for control of an area just north of the capital Sanaa.
They have blown up seven buildings in the Arhab - a district of greater Sanaa - apparently owned by their opponents, despite a ceasefire agreement signed by all parties in September, Al Jazeera sources said.
It comes as Houthi fighters on Sunday sacked the president-appointed governor of Hodeida province Sakhr Alwajih and appointed new new governor loyal to them Hassan Heij.
Houthis on Saturday entered villages in Arhab after tribal leaders in the area decided not to confront the group, sources said.
Mohammed Abdel-Salam, Houthi spokesperson, confirmed that the fighters had taken control of Arhab. The group already controls most of Sanaa and several other cities.
Military and tribal officials said the Houthis used tanks and artillery to shell houses and neighbourhoods of rival tribes.
The fighting left dozens dead, they said.
Amid this backdrop, the Yemeni House of Representatives is expected on Sunday to give the new government a vote of confidence.
Source: Al Jazeera and agencies