"Somaliland forces are carrying out heavy attacks on medical facilities and civilian homes. The deaths and injuries of civilians cannot be counted," said Mukhtar Abdi, a resident of Las Anod, the administrative center of the Sool region.
Local elders in Las Anod said electricity and water had been cut off, and health centers attacked with mortars.
"Today, the (perpetrators) were supported by militias from the neighbouring Puntland region of Somalia and the so called Khatumo militia in a carefully coordinated manner," Somaliland's state broadcaster said on Twitter.
Two doctors said the bodies of 58 people had been brought to their public hospital in Las Anod since the clashes began, with many more injured unable to reach the hospital because of heavy fighting in the town.
On Tuesday Somaliland said fighters from neighboring Puntland, a semi-autonomous region of Somalia, were fighting alongside local militias in the town of Las Anod, accusations Puntland denied.
It was unclear which side started the fighting, but it came a day after a committee of local leaders, religious scholars and civil society groups said in a statement they did not recognize Somaliland's administration.
Puntland's interior minister Abdi Farah Said Juhaa said his government, which has controlled the town in the past, was not involved in the fighting, and that Somaliland should withdraw its troops from Las Anod and other areas.
Somalia's President Hassan Sheikh Mohamud on Tuesday called for a ceasefire: "let the Somaliland administration and the clan elders of Las Anod sit and talk. The solution is in our pursuit of united Somalia."