The clashes broke out on Monday after members of the Believing Youth organisation attacked a checkpoint set up by the al-Majali tribe to keep tabs on the rebels in Saada province in mountainous northwest Yemen.
The incident happened about 40km from the scene of fighting which erupted between the rebels and security forces on 28 March.
Six Believing Youth members and four tribesmen were killed in Monday's firefight in which rocket-propelled grenades and other weapons were used, the witnesses said.
About 110 people have now been killed since the violence erupted in the mountainous region. Intermittent clashes continued on Monday between security forces and followers of Shaikh Husain Badr al-Din al-Huthi, who was killed by the army last year.