The unrest stems from confrontations between government forces from Somaliland and an armed group that swears allegiance to Somalia.
The regular fighting, which flared up on Monday, continued mainly in the town of Las Anod even late on Tuesday.
A local leader said Somali military forces were trying to enter the town of Las Anod, which is currently partially controlled by groups that want the town and Sool region to be part of Somalia.
The unrest broke out after a group of so-called old men called for reunification with Somalia.
UN human rights chief Volker Türk urged those responsible in Somaliland to "with a credible and independent investigation" try to find who was behind the deaths.
Somaliland declared independence from Somalia in 1991, but Somaliland's sovereignty and independence have not been recognized by the international community.