A senior security official, speaking to AFP on condition of anonymity, said the fire broke out in a warehouse located in Al-Russafa, one of the largest voting districts in eastern Baghdad.
Around 60 per cent of Baghdad's two million eligible voters had cast their ballots in the May election in Al-Russafa district.
A column of black smoke billowed from the warehouse, normally used to store foodstuff, and could be seen across the capital.
Two hours after the blaze erupted firefighters, backed by 10 trucks, were still struggling to put out the fire as warehouse staff ran out of the building carrying blue and white plastic ballot boxes, an AFP reporter said.
The cause of the blaze was not immediately known.
It comes as Iraq prepares for a manual recount of around 10 million votes, following allegations of fraud during the May 12 legislative polls.
The vote was won by populist Shiite cleric Moqtada Sadr's electoral alliance with communists, with long-time political figures pushed out by Iraqis voters hoping for change in a country mired in conflict and corruption.
The recount was ordered by parliament on Wednesday at all polling stations, although no timetable has been announced.
According to intelligence services, tests of electronic voting machines -- used for the first time in Iraqi elections -- produced varied results, appearing to give credence to the fraud claims.
"The room where voting machines and other election equipment were stored was destroyed by the fire," Imed Jamil, an electoral commission official for Al-Russafa, told AFP.
"The ballot boxes were stored in another room," he said, adding that the fire would not affect the recount.
"Election material, including maybe ballot boxes, were burned but most of the ballot boxes were stored in another building and have been preserved," Maan told reporters.
Last month's election saw a record number of abstentions as Iraqis snubbed the corruption-tainted elite who have dominated the country since the 2003 US-led invasion that toppled Saddam Hussein.
Less than half of Iraq's 24-million electorate took part, dumping the old guard in favour of Sadr's alliance followed by a list of former fighters of the Hashed al-Shaabi alliance that last year played a key role in the defeat of the Islamic State group.
But the old guard, dumped by Iraqi voters, have clamoured for a recount, although experts say it is unlikely to produce a major change in the number of seats won by their rival lists.
On Wednesday, Iraq's outgoing parliament also sacked the nine-member independent commission which oversaw the polls, and today they were replaced by nine judges who would supervise the recount.
The previous week parliament had already voted to annul the ballots of displaced Iraqis and those living abroad, although they accounted for only a small fraction of the overall vote.
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