Aljazeera's correspondent in Mogadishu, Ehab al-Alfi, reported that 15 people were killed and 40 others wounded in clashes that erupted on Saturday.
Fighting in the centre of Mogadishu had tapered off, but the battleground had shifted 30km north of the Somali capital, he said.
AFP quoted witnesses as saying that the warring factions pounded each other on Saturday with heavy machine guns and grenades in the village of El Arfid, about 20km north of Mogadishu, where the two sides have been battling for control of a key road.
The witnesses told AFP that five armed men were killed and nine people, including two civilians, were wounded, bringing the death toll from clashes in El Arfid and the nearby town of Balad to 19 over the past 72 hours.
Fighters of the Islamic Courts Union, who have been making steady gains in recent days, said they had seized territory but the secular commanders denied it and there was no way to independently confirm the claim.
Witnesses said the clashes which erupted at about 11am (0800 GMT) had subsided by 6pm, but fighters remained on the frontline.
"Today, the casualty figure was low because the area is sparsely populated and people fled on time," elder Mohamed Aden told AFP.
In Mogadishu itself, heavily armed militiamen roamed the streets as war-weary residents cowered in their homes, fearing new clashes in the city a day after imams urged thousands of Muslims to fight the enemy of Islam.
Elders shuttled between the sides seeking a formal truce to cement a tense lull but prospects for a ceasefire appeared slim, with factional commanders re-positioning and re-arming their fighters.
"We are working tirelessly to bring peace to Mogadishu but it seems we are failing," said mediator Hussein Mohamud Dahir, 67.
The US has long viewed Somalia
as a haven for terrorists
At least 332 people have been killed and more than 1,500 wounded, many of them civilians, in three months of battles for control of the city, the bloodiest violence it has seen since the country plunged into anarchy in 1991.
The secular Alliance for the Restoration of Peace and Counter-Terrorism (ARPCT) has received financial and intelligence support from the US and, on Friday, Muslim clerics railed against Washington in a fervent anti-US and anti-alliance protest in Mogadishu attended by some 5,000 faithful.
The alliance, which was created in February, meanwhile, said it would not stop fighting until it has crushed the Islamists.
"We want peace restored in the whole of Somalia," ARPCT spokesman Hussein Gutale Raghe told AFP. "We will not stop until we win."
The US government has long viewed Somalia, without a central government since the 1991 ousting of former ruler Mohamed Siad Barre, as a haven for terrorists.