The AU mission in Somalia (AMISOM) said it had captured the town of Bulomarer, some 160 kilometres southwest of the capital Mogadishu.
The town was the scene of an attempted raid by French commandos in January 2013 to free a secret agent being held hostage.
The bid failed and resulted in the death of two French soldiers and the hostage.
The new offensive is aimed at capturing key ports from the extremist group in an effort to cut off one of its main revenue sources.
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Witnesses reported hearing booms from heavy shelling and seeing convoys of tanks and armoured vehicles southwest of Mogadishu.
AMISOM and Somali government troops were also seen on roads towards Barawe, the last major port held by the hardline gunmen on Somalia's Indian Ocean coast.
"The operations will not stop until the Al-Qaeda militants are eliminated," Nur added.
The Al-Qaeda-linked Shebab are still a powerful and dangerous force but have lost a string of towns to the 22,000-strong AU force.
In previous offensives by AU troops, Shebab fighters have fled in advance of the main column but later returned to stage guerrilla-style attacks.
Shebab fighters continue to launch attacks even in the heart of Mogadishu, including recent brazen commando raids on the presidential palace and parliament.