Partial results of the vote on a new Iraqi constitution suggest at least one Sunni province has rejected it.
Indications suggest the referendum may have been approved
The 20% sample said 81.5% had rejected the draft in Salahuddin, but in Diyala - which has a slight Sunni majority - it was approved by just over 50%.
No figures were given for the other two Sunni provinces of Anbar and Ninevah. A two-thirds rejection of the charter in both would torpedo the project.
As expected, the results suggested a very high approval by Shias and Kurds.
The new Iraqi constitution was meant to help unite the country, but it has proved bitterly divisive, says the BBC's Caroline Hawley in Baghdad.
The Secretary General of the Arab League, Amr Moussa, is on his first visit to Iraq since the US led invasion in a sign of Arab concern over the fragmentation of the country, says our correspondent.
After meeting Shia spiritual leader Ayatollah Ali al-Sistani in the holy city of Najaf, Mr Moussa said he had secured his support for a conference aimed at promoting national reconciliation.
Adil al-Lami of the Independent Electoral Commission of Iraq (IECI) told a news conference he could not give a date for the announcement of final results but said it would take some days.
And he cautioned that the results unveiled on Saturday could not be interpreted either way.
CONSTITUTION'S KEY POINTS
Iraq to be federal, parliamentary democracy
Official languages to be Arabic and Kurdish
Official religion to be Islam but religious freedoms guaranteed
Equal rights for all
Elections every four years
"Let's pretend there are 100 ballot boxes in all Iraq. Well, 20 of those boxes have been brought to Baghdad and these results today represent half of those," Mr Lami said.
"These figures do not show anything much yet."
The official said the count was taking longer than expected because - under international standards - it was necessary to recount the ballots in areas where the "Yes" or "No" vote was very high.
The provisional results showed several provinces approving the constitutional draft with more than 90% - including Najaf with 96%, and Karbala with 90%. In Baghad, the approval rate was 78%.
Mr Lami said no "dangerous" violations of the electoral law had been reported by the complaints.
"We have received more than 100 complaints from different parties... but these complaints are very simple, for very simple violations made by those guarding the elections," Mr Lami said.