The call, from a man whose name is synonymous with the bloody repression of mass protests against his controversial 2009 re-election, marked a new act of defiance against a political establishment that has long since turned against him.
Ahmadinejad made no specific reference in his letter to a wave of unrest that swept Iran over the new year but it comes as the country's divided political factions argue over how to respond.
The Guardian Council is a powerful vetting body which oversees all elections in Iran and which barred Ahmadinejad, among others, from running for president last May.
The council rejected Ahmadinejad's call for early elections and hit back at his criticism of its supervisory procedures.
"The country has no need for... elections right now because all elections are conducted in a legal and sustainable manner," council spokesman Ali Kadkhodai said.
Kadkhodai charged that Ahmadinejad had himself sought to get round the rules in the 2009 election by pressing it to publish the results before the legal time-limit.
The former president referred directly in his letter to a speech Khamenei delivered on Sunday in which he said that progress was needed in "the field of justice", acknowledging widespread criticism of the system.
"These clear comments from the leader can of course be understood" as an appeal for "urgent and concrete reforms that meet the demands of the people," he said.
He also called for the release of all people arrested for criticising the regime and the halting of any proceedings under way.
Ahmadinejad remains popular, particularly among poorer segments of society who recall the large-scale welfare schemes he implemented during his 2005-2013 presidency.
But he has fallen out with the establishment, especially since he ran for president last year against Khamenei's advice.
A number of his senior aides have been arrested on financial and corruption charges, and his protege Hamid Baghaie was sentenced to 15 years in December.
During the 2009 protests against Ahmadinejad's re-election, dozens of people were killed as the regime deployed militia to back up police.
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