His claims were published on Saturday in reformist newspapers and the conservative Jomhouri Eslami, which said the comments came in a speech he made over a month ago that was first broadcast by state television late on Wednesday.
There was no immediate confirmation of the comments from the Iranian presidency or any further reaction on Sunday.
Ahmadinejad has already said he was the target of an assassination plot by Iran's enemies during his visit to Iraq, when he became the first Iranian president to ever visit the country.
"When I was in Iraq… I was told that one of the occupying commanders wanted to see me," Ahamdinejad was quoted as telling commanders from the Iranian volunteer militia the Basij.
"Apparently, he was due to leave on vacation but he had delayed his vacation to see me and I agreed.
"When he saw me, he told me that he was proud of me and said 'you are in our hearts'. Then he asked me to take a souvenir picture with me. And he and his deputy did just that."
"So I patted him on the shoulder and I encouraged him and told him to protect Iraqi people," he was quoted as saying.
Ahmadinejad did not say which country the commanders were from, although the context of his comments suggested that they were supposed to be American.
Jomhouri Eslami, a newspaper close to Iran's hardline establishment, reacted with scepticism to the reported comments.
"If the American commanders are with Iran then how come the Americans wanted to abduct the Iranian president there?" it asked.
Ahmadinejad's remarks were also published in the reformist Aftab-e Yazd, Etemad-e Melli and Sarmayeh newspapers and a video of his speech has been posted on the YouTube video-sharing website.
Ahmadinejad said in June that enemies had planned to kidnap and kill him in Iraq but the plot was foiled after the Iranian delegation changed their travel plans.
Some reformist newspapers openly ridiculed his suggestion, with one saying that if the Americans had wanted to kidnap him they would have done it during Ahmadinejad's annual visit to the UN General Assembly in New York.
His envoy to Rome also said that Ahmadinejad was the target of an "X-ray radiation plot" during his trip to Rome for the UN food summit in June.
