The worst fighting took place around the Holwadag police station, which armed groups attacked with machine guns and rocket launchers.
"We suffered no casualties but a civilian in a nearby house was killed," a policeman said.
Witnesses said rebel fighters also launched a mortar and rocket attack against a Somali security position near a milk factory, killing two soldiers.
An officer who wished to remain anonymous said the burials were already under way and added that a number of other government soldiers were wounded in the incident.
Fighting was also reported near an Ethiopian army post in the Ali Kamin district, where the dead body of a civilian was later found.
A grenade also struck a civilian home in the southern neighbourhood of Shirkole, wounding three brothers, according to the victims' sister.
The latest violence brings to at least 11 the number of people killed in Mogadishu over the past two days.
Instability
Somalia, which is home to about 10 million people, has been plagued by instability that has defied more than a dozen peace initiatives since the 1991 overthrow of former dictator Siad Barre.
More than 1,000 clan representatives from all over the fractious Horn of Africa country have been gathered in the restive capital since July 15 for a reconciliation conference sponsored by the interim government.
The meeting is being boycotted by the government's main Islamist foes, who are planning their own meeting in the Eritrean capital Asmara next month.