The officials, who spoke on condition of anonymity, said the clashes erupted on Monday morning in villages in the northern Arhab mountains after a truce crumbled.
About two weeks ago, members of Houthi and Salafi groups reached a ceasefire agreement after weeks of warfare that killed hundreds of people.
Houthi movement spokesman Mohammed Abdel-Salam accused the Yemeni government of backing the Salafis.
Yemen’s Shia Houthi movement draws its name from the tribe of its founding leader Hussein Badreddin al-Houthi.
The conflict between the government of ousted dictator Ali Abdullah Saleh and Houthi fighters in northern Yemen began in 2004 and ended when a truce was reached in 2010.
In November 2009, Saudi forces also started fighting against the Houthis and bombing their positions after accusing the fighters of killing Saudi border guards.
The Houthis, who control parts of the north and are engaged in reconciliation talks with Sana’a, accuse the government of violating their civil rights and marginalizing them politically, economically, and religiously.
Saleh, who ruled Yemen for 33 years, stepped down in February 2012 under a US-backed power transfer deal in return for immunity, after a year of mass street demonstrations demanding his ouster.
His vice president, Abdrabuh Mansur Hadi, replaced him on February 25, 2012 following a single-candidate presidential election backed by the United States and Saudi Arabia.
The Houthi movement played a key role in the popular revolution that forced Saleh to step down.