Major Barigye Bahoku, a spokesman for the AU mission, said that the al-Shabab group, which is fighting to topple the government, is to blame for the deaths of civilians.
"Too many civilians are caught in the crossfire, but the responsibility for this lies on the destructive extremists who unleash reckless attacks on government and [AU] forces," he said.
Paramedics and police officials in Mogadishu, however, have said some of the shelling is carried out by AU troops.
Human Rights Watch reported in April that AU peacekeepers routinely respond to Al-Shabab attacks by launching indiscriminate attacks into civilian areas.
"AU forces have fired mortar shells into densely populated areas without taking precautions to discriminate between civilians and military targets," the group said. "Such attacks... violate the laws of war."
Afyare Abdi Elmi, a Somalia expert at Qatar University, said the AU assessment was accurate, and that the shelling was beginning to harm perceptions of the AU force.
"At least in the beginning, the AU was not having problems the Ethiopians had. They were not perceived as an occupying force," Elmi said.
"But now with indiscriminate shelling ... this is beyond the limit. It is hurting their perception."
Ethiopian troops invaded Somalia in 2006 to depose the government. Their presence was deeply unpopular, and rights groups say they routinely killed civilians.
Al-Shabab killed 76 people in two bombings in Uganda earlier this month, and said the attack was revenge for civilian casualties in Somalia. Uganda contributes troops to the AU peacekeeping force.