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He declined to speculate on the cause of the crash, but a former defence minister told Reuters he had spoken to a witness at the airfield who said it appeared to have been shot down.
Somalia's al Qaeda-linked insurgency al Shabaab has a presence in the area where the plane came down, although the town of Bardale, in the southern Bay region, and its airfield is secured by Somali forces and Ethiopian troops.
Six people -- the pilot, copilot, flight engineer and a trainee pilot, as well as two people working for the airline -- were onboard, Transport Minister Mohamed Salad told Reuters. Five bodies have been recovered so far, he said.
Salad said he was sending a unit to investigate, who will arrive on Tuesday, and welcomed international assistance.
State-run Somalia News Agency said the plane belonged to African Express Airways and was ferrying supplies for use in the fight against the coronavirus.
"An African (Express) Airways plane from Mogadishu flew to Baidoa and then continued its flight to Bardale town where it crashed," the agency said on its website. "It is not clear why it crashed."
Abdirashid Abdullahi Mohamed, Somalia's former minister of defence, told Reuters he had spoken to a witness at the airfield who said the plane had made an initial attempt to land, had to swing around again due to wildlife on the airfield, and then appeared to be shot on one wing on its second approach.
He provided pictures that showed the plane in flames, pieces of it scattered over a small area and its tail intact, and provided a passenger list with six names. Reuters was unable to immediately verify the images or confirm the names.
Ethiopia has troops in Baidoa and Bardale as part of an African Union peacekeeping mission. The spokesman for the Ethiopian army said he was unaware of the crash.
The al Shabaab insurgency was not immediately available for comment.