The Saeroon Alliance led by al-Sadr, the Shia who many United States military officials hold responsible for the deaths of U.S. troops, won by taking the most number of seats.
Amid allegations of widespread fraud, on Wednesday Iraq's parliament requested a manual recount of around 10 million votes cast.
A fire raged through Baghdad's largest ballot storage site on Sunday, just days after parliament ordered a recount of May's election results amid accusations of fraud.
Warehouse staff ran out of the building carrying blue and white plastic ballot boxes to safety as firefighters backed by around a dozen trucks struggled to put out the fire, an AFP reporter said.
Intelligence services say that tests of electronic voting machines produced varied results, implying the tools may be unreliable.
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The recount was ordered by parliament on Wednesday at all polling stations, although no timetable has been announced.
Sadr's Sairoon bloc won 54 out of 329 seats in the Iraqi parliament.
Abadi's government on Tuesday said an investigation found serious violations and blamed the elections commission for majority.
Opponents of the recount, mostly those whose blocs did well in the election, point out that many who voted for it were lawmakers who lost their seat.
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. The Fatah (Conquest) alliance, led by Badr Organization Secretary General Hadi al-Ameri, and Abadi's Nasr (Victory) coalition finished second and third with 47 and 42 seats, respectively.
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Top Sadr aide Dhiaa al-Asadi said the fire was a plot aimed at forcing a repeat of the election and hiding fraud.
But he has more recently positioned himself as an Iraqi nationalist, critical of both Iranian and American influence and sectarian conflicts in Iraq, and forming diverse alliances with communists, Sunnis and independents. Gen. Saad Maan. Only one, housing electronic equipment and documents, had burnt down.
"The ballot boxes were stored in another room", he said, adding that the fire would not affect the recount.
Before the parliament had acted, the electoral commission said it was voiding 1,021 ballot boxes from around the country, along with votes cast by Iraqis overseas and Iraqis still living in displacement camps that were set up during the battles against the Islamic State. Earlier on Sunday, the Supreme Judicial Council, Iraq's highest judicial authority, named the judges who will take over replace the commissioners.
The electoral commission said it would appeal the decision.
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"There are some papers and equipment of the commision burning in the storehouse that has caught fire", Maan said, according to Rudaw.