The speaker of parliament Salim Al Jabouri has demanded fresh elections.
Iraqi Prime Minister Haider al-Abadi on Sunday claimed the fire was an "intentional plot" targeting Iraq's democracy.
Sadr's warning came as a fire tore through a warehouse in the al-Rusafa district in the Iraqi capital of Baghdad, where thousands of ballot boxes from the May 12 Iraqi parliamentary election were being held. The law called for the Independent High Elections Commission's leadership to be replaced by nine judges.
The timing of the fire undermined the results of an election whose validity was already in doubt. The flames over took the building on the afternoon of June 10, the same day the Judicial High Council was to announce the panel of judges who would be assigned to carry out the recount.
Iraqi cleric-turned-politician Muqtada al-Sadr is looking to strengthen his party's position in parliament, by forming an alliance with two other lists.
"The crime of burning ballot-box storage warehouses in the Rusafa area is a deliberate act, a planned crime, aimed at hiding instances of fraud and manipulation of votes, lying to the Iraqi people and changing their will and choices", he said in a statement.
The political system is created to ensure that no one person or party can dominate, which leads to post-election discussions, a move that has not been interrupted by parliament's decision to recount. Sadr's bloc boycotted the parliamentary session in which the vote took place.
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"Whoever burned the election equipment and document storage site had two goals: either cancelling the election or destroying the stuffed ballots counted amongst the results", he tweeted, suggesting some were trying to sabotage Sadr's gains.
Over 7,000 candidates contested the 329 seats in the parliament that will choose a new president, prime minister and government in Iraq.
Interior ministry spokesman General Saad Maan echoed him during a visit to the scene to the warehouse where the blaze was raging.
Miru Systems, the Korean company that provided the electronic equipment under a $135 million contract, said there was nothing wrong with its system.
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.
"All our options remain open, and they will fall within the parameters of the constitution and Iraqi laws, but we can not predict the reaction and choices of the masses", the leader of Sairoon coalition said in a statement.
"The commission today is targeted from all sides. we call on all constitutional institutions in the country and the leaders of all political blocs to do their historic duty and preserve the results of the electoral process", he said.