The Islamists said that they had captured the headquarters of Abdi Hassan Awale Qeydiid and that his fighters had begun handing over their weapons.
The Islamists have now taken full control of the Somali capital after declaring victory over Qeydiid and fellow warlord and transitional government member Hussein Aidid.
The warlord's positions were attacked on Sunday sparking clashes that forced Qeydiid to flee his tiny stronghold, only to reappear again on Monday.
This was despite an announcement from the Islamists that they had rid the capital of warlords.
A local resident who drove some of the injured to hospital said: "Two civilians passed away steps before they reached Medina hospital, while four other militiamen died in the vicinity."
"People are getting difficult to reach hospitals because of a lack of car movements, and road blocks set up by the rival militia," said Abdi Ibrahim Jiya, a local doctor.
Residents said city streets remained abandoned for fear of sniper fire.
In Nairobi, Kenyan President Mwai Kibaki and his Ugandan counterpart Yoweri Museveni called on the international community to help deploy peacekeepers.
In recent weeks officials from the seven-nation east African Inter-Governmental Authority on Development (IGAD) have complained that the international community, especially Western powers, have been non-committal over the Somali conflict.
IGAD officials said it was complicating regional efforts to restore a functional government in Somalia.
The latest unrest brings the toll to at least 427 dead and more than 2,100 wounded in fighting which first erupted on February 18.