The Antonov-26, which took off from the Turkish city of Adana early on Tuesday, was carrying 35 people, including 30 construction workers, when it crashed.
A Turkish government official said the crash occurred near Balad, the main US military aviation hub in Iraq about 80km north of the capital, Baghdad.
"The plane came down at about midday Turkish time [10:00 GMT] some 2.5km to the northwest of Balad," the foreign ministry press service said.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Turkish officials later put the death toll later rose to 34, although American officials said that one man survived the crash and was being treated.
"Thirty-four people were killed in the accident: an American, 28 Turks and the five crew. There is one survivor, who is seriously wounded," a source at the Turkish embassy in Baghdad told AFP newsagency.
Cahit Kirac, the governor of Adana, told CNN Turk television that the aircraft was carrying 29 Turks, one American and a crew comprising a Russian, a Ukrainian and three Moldovans.
The aircraft belonged to Moldova's Aerian Tur Airlines and the workers on board were from the Turkish construction company Kulak, the Turkish foreign ministry said.