Although estimates vary, it is thought between 102 and 142 people, most of them civilians, have now died since Islamic fighters and US-backed warlords began battling for control of the city, local sources say.
The International Committee for the Red Cross says at least 80 people have been killed since Sunday. A further 200 have been wounded, local hospital sources say.
Both sides engaged in close-range firefights and fired mortars at each other on Saturday night in the northern neighbourhood of Sisi.
Sporadic gunfire was reported in the Huriwa, Waharaade and Yaqshid districts both north and south of the capital.
There are also unconfirmed reports that both sides are massing forces near the road linking the capital to southern Somalia, the only route currently accessible to civilians.
Somalia's largely powerless interim government, based in Baidoa, west of the capital, has urged the international community to help stop the violence.
The street battles are the third this year between militias allied to the Islamic courts and the Alliance for the Restoration of Peace and Counter-Terrorism (ARPCT), who many Somalis believe are backed by the US.
"We... call upon and invite the international community to intervene... by co-operating fully with the Somali transitional federal government to rescue the innocent suffering people," Mohamed Abdi Hayir, Somalia's information minister, said in a statement on Saturday.
"We... call upon and invite the international community to intervene"
Mohamed Abdi Hayir,
Somalia information minister
Washington has long viewed Somalia, without an effective central government since 1991, as a haven for ''terrorists''.