Clashes between gunmen loyal to Mogadishu's Islamic courts and local militia defending the densely populated Yaqshid district began on Saturday and flared again on Sunday.
"The Islamic courts' militia are trying to close all entertainment centres of the district," one local resident Ahmed Dhuhulow told Reuters.
Three people died on Saturday, and another nine on Sunday, in clashes that caused inhabitants to flee the area and shops to close, witnesses and a Reuters reporter said.
Heavy firing could be heard from all over Mogadishu, home to one million of Somalia's 10 million people and scene of frequent street battles during 14 years of anarchy.
"We have not opened the schools this morning, because of the shooting and heavy bullets which are falling down," said school teacher Abdullahi Hassan.
At least two civilians, hit by stray bullets, as well as militiamen, were among the 12 dead, witnesses told Reuters.
The wounded included a child hit by a bullet in the chest.
Leaders of Mogadishu's influential Islamic courts oppose Western and Indian films which they say promote immorality in the mainly Muslim nation.
In the 14th attempt to restore government since 1991, Somalia's new President Abdullahi Yusuf returned from Kenya this year, but has failed to impose authority and has set up base in Jowhar outside Mogadishu due to insecurity in the capital.
Rival warlords have effectively run the Horn of Africa nation since ousting dictator Mohamed Siad Barre 14 years ago.
Islamists have become more prominent during the absence of central authority in Somalia and want the government to ensure a new judicial system based solely on Islamic law.
In Mogadishu, the Islamic sharia courts - along with customary clan law - are the only form of functioning justice.
Politician's son killed
In a separate incident, the son of a senior Somali politician was gunned down on Saturday, his family said.
Unidentified gunmen shot dead Khadar Osman Elmi, son of the second deputy speaker of the Somali parliament Osman Elmi Boqorre, in south Mogadishu, they said.
Speaker Elmi, who has just defected from a Mogadishu-based faction of the new government to the Jowhar group, told reporters he believed the killing was politically motivated.
Besides the Islamic militia's hatred for Western and Indian films, politics may be behind Sunday's fighting, residents said.
One house attacked by the militia was used during a recent visit by Somali Prime Minister Mohamed Ali Gedi, who belongs to the Jowhar group of the divided transitional government.