The fighting for the control of the Somali capital resumed on Wednesday after a five-day lull.
Witnesses and medical workers said the Islamist militia expanded their control of parts of Mogadishu in the battle that began shortly after the morning prayers, capturing a base on a main road linking Mogadishu to Somalia's central region.
The militia also seized at least five trucks mounted with heavy weapons from their rivals, secular armed groups thought to be backed by the US.
Hospital sources said that at least 13 people, mostly civilians, were killed in the fighting.
Somalia has had no effective government since regional commanders overthrew Mohamed Siad Barre in 1991. They then turned on each other, carving the nation into rival fiefdoms.
The power of the Islamist militia, who promise an end to the chaos, is raising fears that the nation could follow the path of the Taliban in Afghanistan.
In the past few days, hundreds have fled Mogadishu to avoid the fighting that has killed at least 83 people since last Wednesday.
About 1,500 people have sought treatment at Mogadishu hospitals for injuries sustained during the fighting since the beginning of this year, UN officials say.