The latest battle is the third between gunmen allied to Islamic courts and militia linked to the Alliance for the Restoration of Peace and Counter-Terrorism, a coalition of powerful armed fighters said to be backed by the US.
Analysts say the upsurge in street battles between the two sides suggests the failed Horn of Africa state is becoming a new proxy battleground for militiamen and the United States.
And a report by a UN Security Council panel released on Wednesday said Islamist fighters have been gaining the upper hand in fighting with foreign-backed warlords and now control roughly 80% of Mogadishu.
The report said the Mogadishu-based opposition had been "severely degraded" by a series of bloody fights with militants' militia, who managed to strengthen their hold over large areas formerly held by the opposition.
It said fundamentalists now control "roughly 80% of Mogadishu" and have emerged as a third force "ideologically motivated and now independent of the opposition but still in opposition to the establishment of TFG (Transitional Federal Government) as a central government".
Siyad Mohamed, a militia leader, said about 80 people were killed and 200 wounded in the run-down area of Siisii before a ceasefire was declared late on Tuesday.
But residents said new fighting broke out in the neighbourhood on Wednesday and battles had erupted in strongholds of Islamic courts in the north of the capital.
Abdullahi Hussein, a local elder, said: "At least 14 people have been killed today."
Although 12 of those killed on Wednesday were fighters, most victims have been ordinary men, women and children.
President Yusuf says the US is
backing the militia
A mortar late on Tuesday struck the Shifa hospital, killing a boy already being treated for a wound from earlier fighting.
Nurto Hussein, the mother of the boy, said: "Even in the hospitals, the bullets are the biggest risk."
Somalia descended into lawlessness in 1991, when militia ousted Mohamed Siad Barre, the former president.
Abdullahi Shirwa, a peace activist, said: "This has caused more deaths and damages than the other two [clashes]."
He was referring to two earlier fights in which more than 120 people were killed.
Many diplomats believe the clashes have been fuelled by US support for the militia, who are reviled by the many citizens who have been terrorised or robbed at gunpoint by their members for the past 15 years.
Washington has long viewed Somalia, without an effective central government since 1991, as a terrorist haven.
The Horn of Africa nation is
home to 10 million people
Abdullahi Yusuf, Somalia's interim president, last week said Washington was backing the militia.
The militia - among them National Security Minister Mohamed Qanyare - call their coalition the Alliance for the Restoration of Peace and Counter-Terrorism in what some say is an effort to win support from the US.
Washington has never directly answered the allegations.
In a statement, the US embassy in Nairobi said: "The United States works with Somalis across the spectrum to support the establishment of the [interim government] and will continue to work with a range of actors from Somali society to address our common concerns, including the war on terrorism."
The violence shows how little control Somalia's fledging government - the 14th attempt to restore rule in 15 years - has over the nation of 10 million.
Formed in Kenya in 2004, the administration has been rendered impotent in all but select areas.