The AU and government forces are attempting to stabilise the Horn of Africa nation which has without an effective central government for two decades.
Al Shabaab, which professes loyalty to al Qaeda, rejected the report by the AU force, which is known as AMISOM, though local residents confirmed the seizure of the district.
"After fierce fighting, the whole of Bondheere district is in the hands of AU and government forces now," said Prosper Hakizimana, deputy spokesman for AMISOM.
Located in north Mogadishu, the district is considered strategic because insurgents use positions there to fire shells at the presidential palace.
Hakizimana said AMISOM tanks and soldiers from the government side were in control of the centre of the district as well as the sites of the former embassies of Syria and Italy.
"We have killed many al Shabaab including foreign fighters," he said, adding they also took casualties, including the death of one Ugandan