"The elders' decision to withdraw fighters and not to fight the Houthis came after a tribal mediation to stop the clashes," the source told The Anadolu Agency.
"Houthi militants, however, are still deployed at several checkpoints and mountainous areas despite the withdrawal of the tribesmen," he said.
Houthi leaders could not be reached for comment.
Earlier Saturday, three Arhab tribesmen were killed when a bomb went off near a vehicle that was transporting them, a tribal source had said.
Several Houthi militants were also killed in the same incident.
The violence came one day after seven Houthis were killed in clashes with tribesmen in the Arhab district.
Since they took control of capital Sanaa in late September, the Houthis have sought to expand their influence to other parts of the country farther afield.
The Houthis' growing power in fractious Yemen has raised fears of sectarian conflict in the poor Arab country, which has remained in turmoil since a 2011 popular uprising ended the decades-long rule of president Ali Abdullah Saleh one year later.