"My government, hereby, calls for the condemnation of such acts of aggression and requests for clear and effective measures to be taken to put an end to these dangerous and unlawful acts in line with the United Nations' responsibilities to maintain international and regional peace and security, in accordance with the letter and spirit of the United Nations Charter," the letter said.
The U.S. Mission to the United Nations was asked for comment on the letter to Ban from Khazaee, but there was no immediate response.
The New York Times reported on Friday U.S. officials viewing the video of the aircraft refused to confirm or deny that it was the one they said was lost by controllers in Afghanistan.
The United States had said it lost control because of a malfunction.
The Times said the aircraft depicted in the video appeared to be in good condition except a close inspection showed what appeared to be tape on a wing, possibly concealing some damage, such as a fracture.
The United States, while not always in the forefront, has been actively against Iran's nuclear program along with its Western European allies. Tehran has long insisted it is strictly for peaceful purposes.
The U.S. spy-in-the-sky down in Iran this week had been looking out for nuclear activity in Iran, rather than monitoring military activity in adjacent Afghanistan, Tehran has said.