The private El Maan port, a trade link to the Gulf and East Africa, remained closed on Friday as gun and mortar fire raged between militia loyal to Musi Sudi Yalahow and the forces of businessman Bashir Raghi.
Attempts by local religious leaders to broker a ceasefire overnight failed and heavy fire was heard from dawn.
Though there were no immediate reports of deaths, medical sources in Mogadishu said more than 55 people were wounded.
Residents said ships due to dock at the port 35km north of Mogadishu remained offshore. Two vessels trying to offload fuel on Thursday came under mortar and rocket fire and pulled back.
El Maan, the country's main maritime port since the official harbour was closed in 1995, is owned by Raghi's cousin Muhammad Umar Aman. Ragh is head of the port's export department.
The fighting has also halted flights in and out of the nearby private Cisaley airfield, local journalists said.
Radio reports said thousands of people had fled their homes to escape the fighting as reinforcements for both sides arrived during Friday.
The factions are using anti-aircraft guns mounted on flatbed trucks and mortars.
Elders related to Musi Sudi, one of Mogadishu's foremost warlords, issued a statement warning commercial operators to stay away from the port until what they termed a land dispute was resolved.
At least 60 people were killed and about 200 injured in fighting in southern Somalia earlier this month.
A country of seven million, Somalia slid into lawlessness with the overthrow of military ruler Muhammad Siad Barri in 1991. Fighting between opposing warlords and famine have killed hundreds of thousands of people since then.