The plane went down near the city of Shiraz and "unfortunately the pilot and the co-pilot were killed," Colonel Hossein Mohammadi, a senior Iranian military official, was quoted as saying, without elaborating.
Iran's Air Force still has several F-4s, manufactured by McDonnell Douglas of the United States and delivered to the Shah before the Islamic revolution of 1979.
Iran is affected by international sanctions imposed as punishment for its nuclear programme, which has stopped the country from buying spare parts for its military and civilian aircraft.
The Air Force has about 300 combat aircraft, including Russian Mig-29s and Su-25s, Chinese F-7s and American F-4, F-5 and F-14 and French Mirage F-1s and some Saeqeh jets, an Iranian version of the F-5.
But many of the planes are not operational, according to experts.