Witnesses said Amisom fired at least 35 rockets into the capital's Bakara market area on Thursday after al-Shabab fighters there launched mortar shells at the aircraft of Sharif Sheikh Ahmed, the Somali president, as he left the airport for a summit in Uganda.
Major Barigye Ba-hoku, Amisom's spokesman in Mogadishu, denied on Friday that the AU soldiers had fired any artillery and blamed Thursday's civilian deaths on bombs of fighters.
"We did not shell any place ... We are investigating and the Somali government is investigating too," he told the Reuters news agency.
"Al-Shabab wants to drag us into their war ... they shell us and then they also shell Bakara, then they tell people there it was Amison who killed civilians. We know their tactics. "
The US accuses al-Shabab, which wants to topple Ahmed's fragile UN-backed administration and impose its own strict verison of Islamic law across the country, of being al-Qaeda's proxy in the failed Horn of Africa state.
About 19,000 civilians have been killed in fighting since the start of 2007 while another 1.5 million have been forced out of their homes.
Somalia, ravaged by drought, has become a safe haven for fighters, including foreign ones, who use it to plot attacks across the region and beyond, Western aid agencies say.
Thursday's clashes were some of the heaviest to rock Mogadishu for weeks, and they underlined the difficulties facing the 5,000-strong AU mission.
Hearts and minds
Amisom has had trouble securing the city's airport, sea port and the presidential palace, although it has won some hearts and minds by giving residents clean water and free medical treatment.
Its soldiers come under near-daily attacks from roadside bombs and rebel artillery.
Last month al-Shabab hit Amisom's headquarters with a twin suicide car bombing that killed 17 peacekeepers, including the Burundian deputy force commander.
"We do not take their threats lightly," Ba-hoku said. "Any attempt to attack Burundi or Uganda will be met with decisive action and will be defeated
" If we get enough troops here, we can move into other regions and bring peace to all of Somalia."
Several African nations had committed to send troops to reinforce Amisom but have so far failed to do so, some saying in private that they are put off by the incessant violence.