Reports that the jet was a US warplane with military personnel on board were contradicted by other sources inside the country, which said its nationality was in fact Hungarian.
Reports said five people were interrogated, but allowed to leave the following day after it became clear their trespass into Iranian airspace had been a mistake.
They added that the interrogation revealed that they had strayed over the border unintentionally en route to Afghanistan.
However, the Pentagon denied that any of its aircraft were missing and it later emerged that the plane was a Falcon passenger jet.
The plane is said to have entered Iranian airspace from Turkey despite repeated warnings by the Islamic Republic Air Force.
Reports said the jet was flying low in an attempt to slip under Iranian radar before being made to touch down.