Violent street battles took place between African Union troops and Islamist rebels, with many running for cover as the sound of heavy artillery could be heard overhead and on the streets from armoured vehicles.
An emergency official said 11 people were killed in one attack when an artillery shell struck a building where families had sought shelter, wounding 22 others.
The head of Mogadishu's ambulance service said the 11 killed included five children and three women.
Six other civilians were killed earlier on Thursday and an additional 21 wounded, the official said.
Radio Mogadishu, the state-run radio station, reported that President Sheik Sharif Sheik Ahmed visited the front lines.
Somalia's fragile, United Nations-backed government has been battling an Islamist insurgency that controls much of the country's south and centre.
The government controls only a few blocks of Mogadishu and relies on African Union peacekeeping troops to protects key government officials and installations.
Somalia has not had a functioning government in nearly 20 years.
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