“This operation is necessary to consolidate the security of Mogadishu,” AU commander Maj Gen Fred Mugisha said as the offensive began.
AU and government forces took control of most of Mogadishu last year.
But correspondents says al-Shabab fighters were able to launch attacks in the city from their Maslah base.
Al-Shabab is under attack on several fronts, with troops from Kenya and Ethiopia also gaining ground recently.
But the group, which joined al-Qaeda last month, still controls much of southern and central Somalia.
It described its withdrawal from Mogadishu last August as “tactical” and has continued to stage suicide attacks in the city.
Somali government forces with the support of AU troops launched the attack on Maslah at dawn, the AU mission in Somalia (Amisom) said in a statement.
Al-Shabab said it had voluntarily withdrawn from Maslah, which is 5km (3 miles) north of Mogadishu on one of two main roads out of the city.
The BBC’s Mohamed Dhore in Mogadishu says two helicopters were used during the offensive.
Amisom said that Maslah was used as an execution ground by al-Shabab.
It also said two AU soldiers were wounded during the operation.
Officials from the UN-backed interim government and workers near the base told the BBC’s Somali Service that loud explosions were heard from Maslah during the fighting.
A similar push two weeks ago was made on the other main road out of Mogadishu heading towards Afgoye, a strategic town held by al-Shabab.
Amisom said this “saw the security cordon around the city expanded”.
Last week, the UN Security Council unanimously agreed to bolster the number of AU forces by more than 5,500 to 17,731 – to include the Kenyan troops that entered the country last October in pursuit of al-Shabab militants.
The resolution passed by the 15-nation council also gave the African force a stronger mandate to attack al-Shabab militants.
Earlier this week, al-Shabab launched a surprise attack using heavy weaponry on a strategic town in the south-west held by Ethiopian troops and local anti-al-Shabab militia.
BBC Somali Service analyst Abdullahi Sheikh says the raid on Garbaharey is a strong indication that the movement’s retreat from key positions does not mean it has given up the fight.
Source; BBC NEWs Africa
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