"It was 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", said outgoing Parliament Speaker Salim Al-Jabouri.
Prime Minister Haider al-Abadi called the blaze a "plot to harm the nation and its democracy".
The latest development comes after a warehouse storing ballot papers caught fire, an act described as a "plot" against democracy by Mr Al Abadi.
An interior ministry spokesman told the Reuters news agency that the blaze had destroyed some documents and equipment, but efforts were being made to stop it from affecting ballot boxes.
Iraqi authorities said the ballot boxes were saved but the fire has added to fears of violence.
A recount would test the number of votes won by Shi'ite Muslim cleric Moqtada al-Sadr, a long-time adversary of USA involvement in Iraq whose bloc, consisting of secularists and Communist Party allies, won the largest number of seats in the election.
The burned ballot boxes are part of a manual recount of votes, after the Iraqi parliament on June 6 approved recount of votes in all polling stations across Iraq over allegations of fraud and irregularities in the May 12 parliamentary election.
The extent of the damage caused to ballot boxes was still unclear but some officials have suggested majority had been spared.
Mr Al Abadi's statement comes as Iraq's United Nations envoy has called for an investigation into allegations of fraud and voter rigging.
"Al-Wataniya Coalition, led by Ayad Allawi, calls for a redo of the parliamentary elections while keeping the current cabinet as a caretaker government to govern the country until the holding of new elections", it read.
Three of the arrested individuals were policemen and one an employee of the Independent High Elections Commission.
The election was the first since the defeat of Islamic State raised hopes that Iraqis could put aside their communal and sectarian divisions and reconstruct the country.
The Baghdad warehouse complex where ballot boxes were stored.
The fire broke out on the same day a panel of judges had been formed to officially take over the election recount from the ostensibly autonomous Independent High Electoral Commission, the body that administered the vote and had since come under intense criticism for its performance.
Certain parties are trying to drag Iraq into civil war, he said, adding that he would not participate in one.
"We call for the election to be repeated", he said.
The election marked the first time Iraqi ballots were counted electronically and not by hand. Some parties condemned the measure, saying it was spearheaded by groups of lawmakers who had lost their seats.