Sheikh Mohamed Ibrahim Bilal, a senior al Shabab official, said: "We killed an uncountable number of government fighters and moderate Islamists. Their dead bodies lie in the streets."
Armed groups in Mogadishu have in recent days intensified attacks against government targets.
Sharif Ahmed, the former leader of the Islamic Court Union, was sworn in as president in January and has pledged to do "everything imaginable" to stabilise Somalia.
He has been trying to broker peace with warring groups and gain legitimacy, but his administration wields little control outside Mogadishu and needs support from African Union peacekeepers.
Fighters opposed to the government see the 4,350 AU peacekeepers as "foreign invaders" and obstacles to peace.