Unidentified witnesses said the conflict began Thursday after one of the insurgent groups attacked a police station in Mogadishu's Yaqshid District, the Shabelle Media Network reported.
The conflict also resulted in dozens of people being injured, witnesses said.
Meanwhile, Ahlu Sunna Waljamaca and al-Shabab fighters clashed Friday in the town of Bardhere. That conflict resulted in two deaths, including top al-Shabab official Abdulahi Fanax.
The conflicts come as Abu Abdullahi Ali, who claims to be an Ahlu Sunna Waljamea spokesman, said the organization's forces in the Bay and Bakol regions are working with government troops, Shabelle said.
The media network, citing witnesses, said Somali Interior Minister Sheik Abdulkadir Ali Omar was injured Thursday in a roadside bombing. The bombing outside Mogadishu killed Omar's secretary.