Islamist insurgents have been engaged in fierce battles with government troops and their Ethiopian allies, and both sides suffered casualties.
Five people were also reported killed when a mortar hit their house.
Correspondents say it is the fiercest fighting for several weeks and has engulfed three separate districts.
Elsewhere, a Somali working for the UN World Food Programme was shot dead as he left a mosque in the central town of Merka, becoming the latest aid worker to be targeted in the war-torn country.
In the capital, an official at the city’s biggest hospital said on Friday it was treating 35 civilians wounded in fighting that began the day before, and that six people had died overnight.
Government forces said one of their soldiers had been killed in the clashes in central Mogadishu and a further two had been injured, the BBC’s Mohamed Ibrahim Moalimuu reports from the Somali capital.
They also said two Islamists had been killed, and that insurgents had been forced to abandon a vehicle mounted with anti-aircraft guns.
At least six other civilians caught up in the fighting in central Mogadishu had been killed, according to witnesses.
Separately, a government vehicle was hit by a land mine and two soldiers were killed.
On Thursday there was also deadly fighting near to African Union peacekeeper bases on the road to Mogadishu’s airport, a key target for rebels in recent weeks.
Ethiopian troops helped the government push Islamist forces from control of central and southern Somalia in late 2006, triggering an insurgency.
The country’s transitional government, which is recognised by the international community, now only controls patches of the country, correspondents say.
Islamists have launched escalating attacks against the AU peacekeeping force in recent months, as well as the government and their Ethiopian allies.
Somalia has been wracked by conflict since President Mohamed Siad Barre was ousted in 1991.
More than three million people – almost half of Somalia’s population – need food aid, according to the UN.
Aid agencies recently estimated that 1.1 million people had been uprooted from Mogadishu over the last nine months.