Most of the casualties were UN contractors who operated near the explosion sites, Xinhua news agency quoted a police official as saying.
The first explosions hit the entrance of the airport while the other one hit a checkpoint nearby, another official said.
There were huge blasts near the airport, a witness said. "I heard two huge explosions and there were bodies of people strewn over the place."
Security forces have cordoned off the area.
Al-Shabaab militant group has claimed responsibility for the attack.
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