Government forces backed by African Union troops retaliated to fend off the insurgents, whose offensive against the presidential compound came as President Sharif Sheikh Ahmed was attending a conference in Turkey.
The Shebab fighters launched their main attack on the northern Shibis and Bondhere neighbourhoods of the seaside capital late Saturday. After a brief lull, the battle resumed at dawn on Sunday.
"The number of civilians killed during the clashes overnight has reached 11 and it could be higher, because the violent militants using mortars attacked several other positions in southern Mogadishu this morning," Mohamed Ali Idle, a Somali government security official, said.
At least three other civilians were killed and 25 wounded as a result of an exchange of mortar fire in the southern neighbourhoods of Holwadag and Black Sea, Ali Muse, head of Mogadishu's ambulance services, said.