The so-called Islamic Army seized diplomat Fereydun Jahani on 4 August as he travelled to take up his position as consul in Karbala.
Iran says it has returned all Iraqis held in its war with its western neighbour and the final group was repatriated last year, shortly before US-led troops invaded Iraq to topple President Saddam Hussein.
"The file concerning prisoners of war between the two countries is closed and all that remains is that of those missing in action," Foreign Ministry spokesman Hamid Riza Asifi told Iran's official news agency IRNA on Sunday.
Asifi described the demand and the nature of the Islamic Army group as "suspicious" and said Iraq's interim government was responsible for securing the diplomat's release.
Iran was in contact with groups it felt could help secure Jahani's release, he said, without giving further details.
Jahani's captors accused him of "inciting sectarian strife and operating outside the sphere of diplomacy".
Iraq's Defence Minister Hazim al-Shalaan has accused Iran of stirring insurrection in Iraq by sending spies and arms across the border.
Washington has also accused Shia Muslim Iran of fomenting unrest among Iraq's Shia community. Iran denies the charges.
Meanwhile, Egypt has been unable to confirm if one of its citizens has been beheaded in Iraq, as claimed by a website.
Foreign Minister Ahmad Abu al-Ghait said on Sunday: "There is no proof an Egyptian citizen was decapitated by an armed Iraqi group who accused him of being a spy for the United States."
A website on Friday broadcast a video which it said showed an Egyptian hostage in Iraq being beheaded by a group belongimg to alleged resistance leader Abu Musab al-Zarqawi.
Abu al-Ghait (L) says there is no
proof an Egyptian was beheaded
The apparent victim, who gave his name as Muhammad Fawzi Abd al-Mutwalli, is seen encircled by three hooded gunmen and confesses in the videotape to having worked as a spy for US forces in Iraq.
After the young man's statement, one of the men steps forward and cuts his neck with a long knife.