The delay came after the independent body said it discovered irregularities in the total number of votes tallied.
"Despite its intention to announce global preliminary results as soon as possible, it needs several more days to complete this difficult and complex operation after finding that figures from most provinces were too high," the commission said in a statement on Monday.
The commission's delay fuelled the Sunni community's allegations of fraud and scrutiny quickly fell on the northern city of Mosul, capital of Nineveh province, 380km north of Baghdad.
Mosul, a multi-ethnic but predominantly Arab city, was one of the hopes of the Arab Sunni community in defeating the draft constitution they say could lead to the fragmentation of the country.
The Association of Muslim Scholars (AMS) argued that the draft included federalist provisions which could lead to the country splitting into three parts - with a Shia south and a Kurdish north holding the oil wealth and the Sunnis left empty-handed in the centre. They urged a no vote.
The Kurds in Mosul and elsewhere overwhelmingly favour the document, as do many within the Shia community.
The draft needs a simple majority of the 15.5 million registered voters for approval. But it can be blocked if two-thirds of voters in any three of the 18 provinces vote against it.
Sunni Arabs have a majority in al-Anbar, Salah al-Din, Nineveh and Diyala provinces.
Voter turnout increases
In January's election, few residents of Mosul voted, although the Kurdish districts of the city headed to the ballot box en masse.
This time, however, Mosul's participation was noticeably different.
Initial results by the city's administration indicated that 70% of the city's registered voters headed to the ballot box.
A few days before the polls opened, many of the city's secular Sunnis debated whether to follow the AMS or the Iraqi Islamic Party which had reached a deal with Shia and Kurdish legislators to amend the wording of the draft.
These include the creation of a panel to consider amendments after general elections on 15 December.
Where is the draft?
In Mosul, however, most voters complained they had not seen the first draft let alone the amended version. Many of the five million copies of the draft the government said it had published for distribution never made it to this northern city.
"I don't know what it says," says Hanaa Ghanim. "How can you ask me to vote on something I never read? I voted 'no'."
But for others, it was not political pressure that influenced their decision.
The electoral commission has
re-examined the vote tally
"We were left with no choice when the copies were not delivered to us but to follow the advice of our religious leaders," said Mohammed Adel, a day labourer.
Adel said he was told by his mosque imam to vote 'yes' the night before the poll because "it was a duty by Allah to vote yes".
"I believe that some voted 'yes' because they wanted to see an end to terrorism and hope the constitution will create a stronger government," he added.
Initial results from Mosul had 70% of the registered voters choosing yes. Later, Sunni officials said they were told by confidential sources within the commission that 55% of Mosul's voters had voted no.
With reports indicating that Salah-al-din and al-Anbar provinces both voting no, Mosul is considered the wild card. If the Mosul vote is majority no, the referendum will have been defeated.
However, if the Mosul tally indicates yes, then the referendum will have passed and Iraqis will look forward to the 15 December general elections.