Sixteen others were wounded in the latest round of fighting, which broke out a day after the leaders of Somalia's three rival factions named mediators for peace talks.
It was not clear when representatives for Hussein Aidid, Ali Mahdi Mohamed and Osman Hassan Ali, known as Atto, would meet.
A militia leader loyal to Ali Mahdi accused Aidid's forces of starting the firefight, which killed three displaced Somalis when mortar rounds landed in a refugee camp.
Since the overthrow of Gen. Mohamed Siad Barre in 1991, Mogadishu has been divided among the three factions, with Ali Mahdi controlling the north and Aidid and Atto each controlling parts of the southern half.
The fighting, which apparently began when Aidid's forces tried to avenge the death of his father, Gen. Mohamed Farah Aidid, at the hands of Atto's men, has claimed about 95 lives in the past week.