The plane was forced to land 16 days ago at the airport of the southern city of Ahvaz due to technical failure, Mahmoud Rasoulinejad, head of the state-owned Iran Airports Company, told the TV station.
Rasoulinejad said three passengers left Iran for Arab countries in the Gulf, but the plane remained under repair in the airport. He said the plane took off from Iran Sunday upon arrival of needed spare parts and completion of repairs.
It was not clear why the announcement of the plane's landing was not made earlier.
Iran is a member of the International Civil Aviation Organization, or ICAO, which requires members to come to the aid of civilian aircraft when requested.
The service was provided though Iran and U.S. are at odds over Tehran's suspect nuclear program. The West believes it might be aimed at weapons development, a charge Iran denies.
A separate report by state TV said the Falcon-900 plane had one passenger and two crew members and was flying to Rotterdam in the Netherlands from Abu Dhabi in United Arab Emirates when it encountered mechanical difficulties.
It said a French team from Abu Dhabi repaired the plane at Ahvaz airport.
Every day some 500 foreign airplanes pass through Iranian airspace, including 30 American aircraft.