Ahmadinejad wrote that despite early promises by the US president to improve ties with Iran "the same hostile policies along with the same trend of enmity were pursued".
He specifically mentioned the $2 billion of Iranian foreign currency reserves seized from New York bank accounts earlier this year.
In April, the US Supreme Court confirmed an earlier ruling that the money should be used to compensate the families of victims of the 1983 bombing of a US Marines barracks in Lebanon and other incidents blamed on Iran.
Iran is appealing the decision at the International Court of Justice.
"I passionately advise you not to let the historical defamation and bitter incident be recorded under your name," Ahmadinejad wrote.
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The letter comes as the controversial former president, who led the country from 2005 to 2013, is reportedly working towards a possible run in next year's presidential election.
He has made multiple public appearances around the country in recent weeks, although he has yet to formally announce he is running.
Ahmadinejad's inflammatory rhetoric -- particularly regarding Iran's nuclear programme and hostility towards Israel -- was blamed for deepening tensions with the West, but his populist approach and humble roots means he has retained popularity with poorer sections of Iranian society.
By the end of his term, Ahmadinejad had alienated even the conservative establishment and it remains to be seen whether he will be approved as a candidate by the powerful Guardian Council.
The council announced last month that the election will take place on May 19.
President Hassan Rouhani, a moderate who oversaw a deal with world powers to end sanctions in exchange for curbing Iran's nuclear programme, is expected to run for a second term, although he faces mounting pressure from conservatives who say the deal has brought few benefits to Iran.