The officials say today's clashes were in Amran province, one of three fronts where battles are raging between Hawthi rebels and Salafis.
Two other fronts with sporadic fighting are in the adjacent Saada and al-Jawf provinces, bordering Saudi Arabia.
The officials spoke on condition of anonymity because they were not authorised to speak to the press.
President Abed Rabbo Mansour Hadi is expected to send mediators.
The fight over the northern region is taking a sectarian undertone as Salafis are accused of trying to spread their school of thought in a stronghold of Hawthis, who belong to the Zaydi sect.