In a statement, the AU called for a no fly-zone along with a sea blockade off Somalia to stem the flow of weapons from Eritrea, which denies supporting the Islamists.
Eritrea has recalled its AU ambassador in retaliation.
Hizbul Islam and al-Shabab fighters, linked to al-Qaeda, have in recent days intensified their offensive against the new government of Sharif Ahmed, the Somali president.
Somalia's neighbours and Western governments fear the Horn of Africa nation, mired in civil war for 18 years, could become a haven for Islamist fighters unless the new government can defeat them.
Barigye Bahoku, the AU peacekeeping force spokesman in Mogadishu, told Al Jazeera the fighting had been going on for the past three days.
He said government forces had reorganised themselves and relaunched an offensive to recapture the areas that had been taken earlier by the forces opposed to the government.
Bahoku said the role of the African Union Mission in Somalia (Amisom) was "surely not there".
"What can we do? We are doing what we were mandated to do. We cannot adjust our mandate or operate outside it," he said.
"We feel frustrated; we feel anger that the whole of this world is being held at ransom by about 2,000 armed people beginning with their own nationals - the Somalis - and ... the impact is felt by the rest of the world, including you and me."
The AU, which has some 4,300 peacekeepers from Burundi and Uganda in Mogadishu, is protecting key sites but its mandate limits the force to defending itself when attacked.
But Mohamed Abdi Gandi, Somalia's defence minister, struck an optimistic note and insisted that government troops would defeat anti-government fighters.
"It was our plan to make peace in our country and restore law and order," Gandi said.
"Our security forces, with the help of our people in the operation, have reached their target and are in defensive positions."
A human rights group said a lull in the violence on Saturday saw many residents fleeing, joining thousands of others who have left the city.
|Many residents fled during a lull in the
fighting on Saturday [Reuters]
Ali Addeh, deputy director of Medina Hospital, said he had recieved 195 wounded civilians, 21 of whom had been discharged after treatment.
Heavy gunfire and explosions could still be heard in Mogadishu as people fled.
Islamist fighters took up arms in 2007 to drive out Ethiopian troops propping up a Western-backed government which failed to wield control over much of Somalia.
Since the start of 2007, fighting has killed at least 17,700 civilians and driven more than one million from their homes.
About three million Somalis survive on emergency food aid.
The Ethiopians withdrew at the start of 2009 leaving Somalia as they found it - in chaos and with virtually no central government.