Most of the dead and wounded were children leaving a video arcade, said Capt. Mohammed Hussein, though he couldn't say precisely how many of the causalities from the attack were children.
At the scene of the blast, a screaming, bloodied child was taken away in an ambulance. His sobbing mother buried her head in grief near the wreckage of the twisted car bomb.
"Is my son a government soldier?" she asked a reporter. "Those who attacked here only wanted to see dead children and mothers, not government people."
The car bomb attack comes after a bomb blast in Mogadishu on Sunday that killed 15 people.
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The Islamic extremist group al-Shabab continues to carry out bombings in Somalia's capital as the rebels continue to lose territory to African Union and Somali forces in the countryside.
Such attacks are an effort by al-Shabab to deny the Somali public "any sort of life and freedom," said Hussein. "They are targeting public places and soft targets now," he said.
US forces last month killed the head of al-Shabab in a bombing run but the group quickly named a new leader.