Somali government forces supported by AMISOM troops "on Thursday captured the Damanyo military camp also known as Shirkole Ofishiale, the last remaining outpost" of the Al-Qaeda-linked Shebab in the western part of Mogadishu, AMISOM spokesman Major Paddy Ankunda said in a statement.
"This gives the Somali government full control over Terebunka Road," a major thoroughfare that links the north of the city to a strategic crossroads in the centre, the statement said.
An AFP correspondent in Mogadishu confirmed MISOM's advance.
Thursday's fighting left at least 17 civilians dead. No casualty figures were available for fighters on either side.
Sporadic gunfire could still be heard Friday in the area where the fighting took place.
Terebunka Road controls the western access to Bakara market, the biggest market in the city and a major source of revenue for the Shebab.
"The road will soon be reopened to civilian traffic once mopping-up operations to ensure safety are complete," AMISOM Chief of Staff Colonel Innocent Oula said.
AMISOM, now made up of some 9,000 Ugandan and Burundian troops, has been deployed in Mogadishu since 2007 to support the fragile transitional government of Sharif Sheikh Ahmed.
In a series of operations carried out since late February, AMISOM troops have pushed back the Shebab on the two main front lines in Mogadishu and now control around half of the capital.
AMISOM's Burundian contingent, deployed in the north of the city, and its Ugandan contingent, closer to the centre, "have linked up and are presenting a common front," Oula said.
Somali pro-government forces, made up of the army as well as clan and religious militia groups, have played a marginal role in the advances.