The ballot boxes were being taken to Baghdad on Tuesday to be checked by election officials investigating "unusually high" vote totals in areas said to be predominantly Shia and Kurdish provinces, where as many as 99% of the voters reportedly approved Iraq's draft constitution.
The investigation by Iraq's election commission, which was announced on Monday, has raised the possibility that the results of the referendum could be called into question.
"The sandstorm ended Monday night, ballots boxes are now arriving here again from the provinces, and our employees have resumed their counting," said Adil al-Lami, head of the Independent Electoral Commission of Iraq.
"If we suspect that the numbers are higher or lower than we expected, we have to double-check them, and this audit means it might be several more days before we announce the final outcome," he said.
"We are not concerned whether the outcome is 'yes' or 'no'. We are only interested in making the process technically a success."
He said the commission was a neutral body acting as a referee.
Questions about irregularities
The investigation by the commission has raised questions about irregularities in the balloting.
Word of the review came on Monday as Sunni Arab leaders repeated accusations of fraud after initial reports from the provinces suggested the constitution had passed.
Among the allegations are that police took ballot boxes from heavily "no" districts and that some "yes" areas had more votes than registered voters.
The electoral commission made no mention of fraud, and an official with knowledge of the election process cautioned that it was too early to say whether the unusual numbers were incorrect or would affect the outcome.
But questions about the numbers raised tensions over Saturday's referendum, which has sharply divided Iraqis.
"This audit means it might be several more days before we announce the final outcome"
Independent Electoral Commission of Iraq head
Most of the Shia and the Kurds - the coalition that controls the government - support the charter, while most Sunni Arabs sharply opposed a document they fear will tear Iraq to pieces.
Irregularities in Shia and Kurdish areas, expected to vote strongly "yes", may not affect the outcome.
The main electoral battlegrounds were provinces with mixed populations, two of which went strongly "yes". There were conflicting reports whether those two provinces were among those with questionable figures.
At Baghdad's counting centre, election workers were cutting open plastic bags of tally sheets sent by plane and helicopter from provincial stations.
Nearby, more workers, dressed in white T-shirts and caps bearing the election commission's slogan, are sitting behind computer screens punching in the numbers.
Election officials in many provinces have released their initial counts, indicating that the charter has been approved.
But the commission found that the number of yes votes in most provinces appeared unusually high and would be audited, with random samples taken from ballot boxes to test them.
The high numbers were seen among the nine provinces of the south and the three in the north, al-Lami said.
Up to 98% say yes
Those provinces reported to AP yes votes above 90%, with some as high as 97% and 98%.
Two provinces that are crucial to the results - Ninevah and Diyala, which have mixed Sunni, Shia and Kurd populations - were not among those that appeared unusual.
Iraqi election employees have
started counting the votes
But the official with knowledge of the counting process said the unexpected results were not isolated to the Shia and Kurdish provinces and were "all around the country".
Sunni opponents needed to win over either Diyala or Ninevah to veto the constitution.
Sectarian balance unknown
Sunnis had to get a two-thirds no vote in any three of Iraq's 18 provinces to defeat the charter, and they appeared to have got it in western Anbar and central Salah al-Din, both Sunni.
Ninevah and Diyala are each believed to have a slight Sunni Arab majority.
But results reported by provincial electoral officials indicated startlingly powerful yes votes of up to 70% in each.
Allegations of fraud in those areas could throw the final outcome into question.
But questions of whether the reported strong yes vote there is unusual are complicated by the fact Iraq has not had a proper census in 15 years, meaning the sectarian balance is not firmly known.