Iranian news agencies said it was a military cargo plane carrying meat from Kyrgyzstan's capital of Bishkek. Authorities did not immediately offer a reason for the mistake, though they said the Iranian crew had declared an emergency prior to landing.
The airport is located near Karaj in the central province of Alborz.
Officials are continuing to search for bodies in the wreckage.
The army's statement came after some confusion over who owned the plane.
Iran's Red Crescent Society has dispatched eight rescue teams, including several ambulances and a helicopter, to the site.
State broadcaster IRIB earlier said there were 10 people on the plane, without confirming any casualties.
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Dane's Range Rover was later found by police on Bowland Drive in Fallowfield but Taylor's white BMW is yet to be recovered. Three people were injured in the raid, police said, although it is unclear if the footballer's brothers were hurt.
"It exited the runway during the landing and caught fire after hitting the wall at the end of the runway", the army.
Dramatic pictures show how the plane slammed into a building after overshooting the runway. Images carried by Iran's state-run media showed the burned-out tail of the plane sticking out, surrounded by charred homes.
But a source told Fars agency that the plane belonged to the Iranian military's air force.
It was later confirmed it belonged to Iran's air force.
There were no reports about the fate of those on board.