Ahmadinejad has applied for a U.S. visa to attend a nuclear conference at the United Nations next week.
The mothers of Shane Bauer, Sarah Shourd and Josh Fattal sent him a letter this week, asking the Iranian leader to bring their children with him to New York.
They say it "would be a most noble act of mercy and compassion."
The three have been held since crossing the border from Iraq in July. Their families say they unintentionally strayed while hiking.
Iranian officials have suggested the three may have links to U.S. intelligence, a claim the families say is absurd.
Fattal's family lives near Philadelphia, Bauer's in Pine City, Minnesota, and Shourd's in Oakland, California.
