Witnesses and clan elders said the clashes in the central Galgudud region and the northern town of Beletweyne were between rival militias over unsettled scores and banditry, and not linked to disputes over the war-shattered country's transitional government in exile.
On Tuesday in Galgudud, a brief but intense battle between fighters from two subgroups of the Hawiye clan killed 12 people and wounded 18 others, said Mumin Hadji Ali, an elder from a neutral faction.
"We don't know who started the fighting, but each side says it was attacked first," Ali said.
Another witness, who did not want to be named, said the fighting was heavy and had erupted despite a truce agreement the two sides had reached two months ago.
After a lull of several hours, fighting between gunmen from the rival Galjeyil and Jajolo resumed on Tuesday at the Beletweyne trading post about 300km north of Mogadishu, witnesses said.
On Monday, fierce clashes there killed 18 people, including a child, and wounded 23, according to Elmi Yassin, a businessman in Beletweyene who was trying to mediate in the dispute.
Some witnesses said the fighting was linked to banditry, while others blamed it on long-running disputes over water and access to pastures.
Somalia has lacked an effective central government since the 1991 ousting of president Mohammed Siad Barre split the vast desert country of 10 million people into a patchwork of fiefdoms governed by regional leaders.
Somalia's new leaders, who were sworn into office in Kenya last year, are still based in Nairobi because of widespread insecurity in their own country.