It was not immediately clear who was behind Wednesday's attack, which came minutes after a United Nations delegation arrived at the airport.
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Meanwhile, the Washington Post and other news agencies are reporting the U.S. staged another air strike Monday against suspected al-Qaida operatives being shielded by Islamic militants in southern Somalia.
The United States carried out a similar strike earlier this month. A Pentagon spokesman would not confirm the report, saying only that the United States continues to work with countries in the region to seek out, capture and, if necessary, kill all al-Qaida operatives.
On Tuesday, Ethiopian troops began pulling out of Mogadishu in anticipation of the deployment of 8,000 peacekeepers from the African Union.
Ethiopian Prime Minister Meles Zenawi says the withdrawal is being timed to coincide with the arrival of AU forces, to ensure there is no security vacuum.
Somali interim government troops and Ethiopian forces seized control of Mogadishu and surrounding areas late last month, after a two-week battle against the Islamic Courts movement.
The Islamists who fled Mogadishu have threatened to wage a guerrilla war against the interim government and Ethiopian troops still in the country.
Somalia has been without an effective central government since warlords overthrew dictator Mohamed Siad Barre in 1991.