The brief video, aired on the Arabic-language Al-Alam TV, shows what the channel says are parts of the drone, scattered in an unidentified desert area.
A scroll accompanying the footage says the drone was downed on Saturday and identifies it as a Hermes 450, a known Israeli model. The Iranian TV also says the model is dubbed "Spy Goddess."
However, there were no visible Israeli markings in the footage and Israel's military has declined comment on the matter. Calls by The Associated Press to Iranian officials for details on the drone were not immediately returned. The aircraft was not shown to foreign media.
Israel has not ruled out taking military action against Iran's nuclear facilities if its capability to build an atomic weapon progresses.
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The West suspects Iran's nuclear program is geared toward building a nuclear weapon. Iran denies the charge, saying its nuclear activities are for peaceful purposes only, such as power generation and medical research.
The Guard statement yesterday said its forces fired a missile as the drone neared Iran's uranium enrichment facility in Natanz, some 240 kilometres south of the capital, Tehran, without providing more details.
Hajizadeh said the drone's range was about 800 kilometres and that it had two front and side cameras capable of providing high-resolution panoramic imaging. Israel is about 1,000 kilometres away from Iran's westernmost boundary and Natanz is about 600 kilometres inland from the closest border point in Iran.
"The operational range of the drone indicates it did not start its flight in Israel but departed from a country in the region," he said, adding cryptically, "We have some clues."
Iran says it and other computer virus attacks are part of a concerted effort by Israel, the US and their allies to undermine its nuclear program through covert operations. Israel has never commented on the allegations but is widely believed to have been involved in the Stuxnet attack.