An Iraqi army plane crashed on March 16 near the oil city of Kirkuk, with the military blaming a technical problem but the Islamic State (IS) said its fighters shot it down.
Military sources the plane was on a "reconnaissance and combat" mission, and that its three crew are considered missing.
The Cessna 208 Caravan, in its combat version, can be used to launch laser-guided Hellfire missiles.
An IS video on Twitter showed a plane falling to the ground and claimed that IS fighters had shot the plane down, killing five crew members.
IS claimed it used anti-aircraft artillery against the plane, which it said had been bombing the city of Hawijah, an IS stronghold in Kirkuk province.
The video shows the wreckage of a plane that could be a Cessna Caravan, with IS fighters celebrating around body parts.
IS shot down an Iraqi military helicopter on February 17, killing two crew members.
Two days earlier, an Iraqi Mi-17 helicopter crashed south of Baghdad due to what officials described as a "technical problems," killing nine people.