Machine guns, rocket-propelled grenades and mortars were used in the fighting after the fighters ambushed forces patrolling a road near the presidential palace.
"The fighting is very heavy in a way we have never experienced in recent months. I have seen three civilians killed," Mohamed Younis Ali, a resident of Taleh district, said.
On Monday, Nur Hassan Hussein, the Somalia prime minister, and Sheikh Sharif Ahmed, leader of the Alliance for the Re-liberation of Somalia (ARS), signed agreements at UN-sponsored talks in Djibouti, Ethiopia, which included a three-month truce which is to come into force at the end of the month.
The AU has deployed about 2,600 peacekeepers in Somalia - short of the pledged 8,000 troops.
But they have failed to stem the violence, which rights groups say has killed 6,000 civilians over the past year.
According to the truce deal, Ethiopian forces will withdraw after the UN deploys peacekeepers.
The UN Security Council is considering a peacekeeping force but no concrete decision has been made yet.
Somalia's transitional government, formed in 2004 with the help of the UN, has been fighting the Islamic courts after they seized control of the capital and most of southern Somalia in 2006.
The government called in troops from neighbouring Ethiopia to help push them out of Mogadishu.