The Independent Electoral Commission of Iraq said today it had found no instances of serious fraud in the constitutional referendum and was still verifying some results only because of statistical issues.
IECI commissioner Adil Al-Lami said it would take some days before there was a final announcement of results but gave no date.
He gave partial results for 13 of Iraq's 18 provinces, of which only one returned a two-thirds majority "no" vote.
Two more provinces would need to do so in order to block the constitution.
Mr Lami told a news conference only a small proportion of ballots had been brought to Baghdad and the results published so far were extremely limited.
"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."
He gave no figures at all for five provinces, including the largely Sunni Anbar, which is expected to have voted no, and the mixed province of Nineveh, which is viewed as the only other one that could possibly give a two-thirds majority no vote.
Electoral officials have said privately they believe the constitution will be ratified.
Drawn up as part of the US-backed drive to strengthen the political process in Iraq, the constitution exposed deep divisions between the country's Sunni Arab minority and the Shia and Kurdish communities.
Provisional figures indicated that most provinces returned a "Yes" vote.
Salahaddin voted by more than a two thirds majority "No" and Anbar is also expected to have done so. Mr Lami said the count was taking longer than expected because under international election standards it was necessary to recount the ballots in areas where the yes or no vote was very high - several provinces returned majorities of over 90 per cent.
Investigators were looking into some of those provinces and were also doing random checks on the ballot boxes, he said. But he emphasised the checks were due to "statistical issues" and played down suggestions of irregularities, noting that representatives of all parties had been present as observers at polling stations.