The leader of al Shabab - Sheik Muktar Abu Zubayr - also thanked the militants who carried out the bombings, which killed 76 people.
In an audio message played on Mogadishu radio stations, Abu Zubayr told Uganda's president that the attacks were only the beginning.
The bombings ripped through a restaurant and rugby club, leaving many injured, including several Americans.
Al Shabab said the bombings were revenge for Uganda's deployment of peacekeepers in Mogadishu.
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