There were 16 people onboard and only the flight engineer survived, according to Fars news agency, which is considered close to the military.
A spokeswoman for Kyrgyzstan's Manas airport said the plane, en route from Kyrgyzstan's Manas airport, belonged to Iran's Payam Air.
The army's statement came after some confusion over who owned the plane.
Fath airport is near Karaj in the central province of Alborz.
Officials are continuing to search for bodies in the wreckage.
The TV says a fire engulfed the plane immediately after the crash in the town of Safadasht.
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TV said rescue teams had been sent to the area, between the airports of Fath and Payam.
Earlier, local media had reported that at least 10 people were onboard without confirming any casualties.
The plane's engines and wheels are spread across the crash site and images from inside the plane's hull show it is completely charred.
But a source told Fars agency that the plane belonged to the Iranian military's air force. The Iranian air force does operate Boeing 707s; it also has a civilian airline, SAHA.
There were no reports about the fate of those on board.
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