More than 1,000 troops, backed by African Union peacekeepers, and 20 tanks attacked areas of Mogadishu where militants had been hiding since they were pushed back last year, the Shabelle News Network reported.
Al-Shabaab, linked to al-Qaida, controls large areas of southern and central Somalia but the group has been under attack on several fronts and Somali authorities say they are gaining the upper hand.
The conflict has no front lines and suicide bomb attacks by the militants make it difficult to completely secure the city, the BBC said.
Six people died Thursday in a suicide bomb attack on a refugee camp in Mogadishu, the BBC said.
Notable deaths of 2014 [PHOTOS]
Syrian Al Qaida group executes Lebanese soldier