But the US defence department said it was unaware of any US military aircraft being forced to land in Iran and that all US aircraft in the Gulf region were accounted for.
Lieutenant-Colonel Patrick Ryder said: "According to the combined air operations centre, all our aircraft are accounted for and we have no reports of any aircraft landing in Iran."
Hungarians
A senior Iranian official denied Fars' report on Tuesday, saying both the aircraft and the people on board were Hungarian.
"The Fars report was not accurate. It was an Hungarian aid plane. No American was on board. The incident happened on September 30," the Iranian official, who declined to be named, said.
Fars reported that the jet was carrying five military officials and three civilians from Turkey to Afghanistan when it "unintentionally" entered Iranian airspace.
Iranian fighters guided the jet to an Iranian airport, the passengers were questioned and a day later were released and allowed to continue to their destination, Fars said.
It said the jet was a Falcon, apparently referring to a passenger aircraft manufactured by the French firm Dassault.
'Lost its way'
Al-Alam, Iran's official Arabic-language television station, quoted an unnamed military official as saying that the jet belonged to either a British or Hungarian relief agency.
He said the aircraft "lost its way" and violated Iranian air space. He said the passengers included American military personnel but did not elaborate.
"This plane was not a military plane and did not belong to the United States," the official was quoted as saying by Al-Alam.
The aircraft was forced to land in Iran on Sunday and allowed to fly to Afghanistan on Monday, the website said.
Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said: "The plane entered Iranian airspace via the Turkish border. Iran noticed it and forced it to land.
"After interrogations were completed, it was clear that they entered [Iranian airspace] unintentionally, with their destination being Afghanistan."