Salim al-Jubouri, the outgoing speaker of parliament, who lost his seat in the election, called for an entire redo of the vote because of the fire.
Parliament has already ordered a recount of votes from the May election, in which the influential cleric Moqtada Al-Sadr was the biggest victor, after widespread allegations of voter fraud.
Videos shared on social media showed civil firefighters removing ballot boxes from the site.
A fire ripped through Iraq's biggest ballot warehouse on Sunday where votes for the eastern Baghdad district were stored, before a recount ordered by parliament, a security official said. But ballot boxes apparently have not been destroyed.
In the days after the election, reports of fraud began to emerge primarily from the Kurdish region of northern Iraq, while voters nationwide complained about difficulties using the electronic voting machines that were being used for the first time.
Confusion has gripped Iraq since the vote won by Shia cleric Muqtada al-Sadr's electoral alliance with the Iraqi Communist Party, even with negotiations to form a new government underway.
On Tuesday, Prime Minister Haider al-Abadi warned that security agencies had evidence of "unprecedented" violations.
Opponents of the recount have pointed out that many of those who voted for it lost seats in the election.
The previous week parliament had already voted to annul the ballots of displaced Iraqis and those living overseas, although they accounted for only a small fraction of the overall vote.
Jabouri's call was seconded by Vice President Iyad Allawi, the leader of the electoral alliance Jabouri ran as part of.
Interior ministry spokesman General Saad Maan echoed him during a visit to the scene to the warehouse where the blaze was raging.
The SJC convened on Sunday to name the judges and to meet with officials from the electoral commission to "understand how it works and get a briefing on the nature of complaints it received regarding the 2018 legislative elections", the statement said.
More than 170 MPs voted in an emergency parliamentary session on Wednesday to amend the law, which will also nullify votes cast overseas and from displacement camps in four Sunni-majority provinces. Only one - housing electronic equipment and documents - had burned down, he said.
On Wednesday Iraq's parliament ordered a manual recount at all polling stations - although no timetable has been announced - and sacked the commission which oversaw the polls.
Last week, Iraq's parliament voted to dismiss the commissioners and replace them with judges while calling for a full hand recount of about 11 million votes.
The electoral commission said it would appeal the decision.
"The fire does not affect the election results", Maan al-Hetawi said, because it had kept copies of the paper tallies produced by the vote counting devices in a separate location.
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