"Puntland and Galmudug soldiers fought for close to an hour in the Sahaa area of the Mudug region and three soldiers lost their lives," Said Muse, a Galmudug State administration official, told The Anadolu Agency.
Two other soldiers had been seriously injured, he added.
Somali clan elders met later in hopes of resolving the conflict, although tension remains high.
Somalia's federal constitution calls for the formation of semi-autonomous regional states, each headed by a president and each maintaining its own army.
Clashes have broken out in the past between Somali regional states, mostly over natural resources or due to clan rivalries.