"It is possible there were also some ballot boxes in the warehouse that caught fire, but most of the important boxes are in the three warehouses, where the fire has been controlled", he said.
This comes as the Iraqi Supreme Judicial Council named nine judges to take over the country's electoral commission's work on Sunday amid widespread allegations of fraud.
Videos shared on social media showed civil firefighters removing ballot boxes from the site.
The site was divided into four warehouses, said Major General Saad Maan, and only one - housing electronic equipment and documents - had burned down.
Sunday's fire broke out at a Trade Ministry site in Baghdad where the election commission stored the ballot boxes from Al-Rusafa, the half of Baghdad on the eastern side of the Tigris river.
The parliament voted in favor of a nationwide manual recount last Wednesday after Prime Minister Haider Al-Abadi, whose coalition came third in the voting, said the recount was necessary considering the reported violations. "Corrupt elected politicians set the ballot box fire to preserve their political interests", said a 53-year-old policeman who gave his name as Abu Zeinab.
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. The move could further delay the formation of a new government as well as cast a shadow over Iraq's fledgling democracy.
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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. That faith was already low, he suggested, given a low turn out of 43 per cent.
A ticket backed by the Shiite cleric Moqtada al-Sadr, a longtime opponent of American influence in Iraq, won the most seats in the initial count, with 54 out of 329 - placing him in prime position to select the nation's next leader.
But the results have been marred by lingering allegations of voter fraud.
It comes amid mounting fraud allegations surrounding the 12 May elections, when Sadr was announced the surprise victor of the vote.
"We call for the election to be repeated", added Jabouri, who lost his seat in the election.
Intelligence services say that tests of electronic voting machines produced varied results, implying the tools may be unreliable. Mr Al Jabouri was not reelected during the May 12 vote.