The fire in Baghdad, at one of the ballot warehouses, has fueled even more claims of a cover-up of the results.
"Burning election warehouses.is a plot to harm the nation and its democracy", Abadi, whose coalition faltered in the polls by finishing third, said in a statement on Sunday. "We will take all necessary measures and strike with an iron fist all who undermine the security of the nation and its citizens", said Abadi late on Sunday.
However, an interior ministry spokesman Major General SaadMaansaid that the fire had destroyed some documents and equipment but first responders on the site were trying to prevent it from spreading to ballot boxes.The warehouse is one of four at the site and contained documents and electronic equipment.
"I can tell you all the boxes and papers have burned", Mohammed al-Rabeei, a Baghdad province council member, told Al Jazeera.
Iraq's parliament speaker, Salim al-Jabouri, has since called for an election rerun in the wake of the fire.
Mr Al Abadi said only the Supreme Court could decide whether to re-run the ballot, which was won by Shiite cleric Moqtada Al Sadr's Sairoun bloc, after the parliament called for a nationwide recount of the votes.
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"It is not an ideal situation for Iran and they might support a redo, but actually a recount might implicate them if the allegations in the north are correct".
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.
Iraq's Independent High Elections Commission had used electronic vote-counting devices for the first time in the May 12 election.
The fire started hours after a number of judges were officially tasked with carrying out the manual process of recounting the votes from May's election.
Iraqi authorities said that none of the ballot papers were destroyed in the blaze.
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 a year ago played a key role in the defeat of the Islamic State group. The Fatah Alliance, led by Hadi al-Amiri, took 48 seats, while the Victory Alliance, led by Washington's preferred candidate, Prime Minister Haider al-Abadi, won 42 seats.
"Is it not time to stand as one for building and reconstruction instead of burning ballet boxes or repeating elections just for one seat or two?" he added.
But a repeat of the election is unlikely, analysts say, as none of the top parties have endorsed this step, and many incumbent lawmakers have lost their seats and thus lack legitimacy in the eyes of the public.