Iraq's constitution looks set to be passed despite strong opposition from Sunni Arabs who turned out in high numbers in an effort to stop it.
The United States has praised the Iraqi people for turning out to vote in spite of insurgency violence.
But Sunni leaders are warning that the vote could divide the country further.
Early counts have indicated that the vote was split along communal lines, reflecting the bitter ethnic and religious tensions that have cost thousands of Iraqi lives since the US-led invasion in 2003.
High votes in favour of the constitution have been recorded in mainly Shi'ite southern provinces and are also expected in Kurdistan.
Despite high turnout in some Sunni Arab areas, partial counts suggest the charter's opponents did not muster enough 'No' votes to veto it.
According to the referendum rules, a two-thirds 'No' vote in three of Iraq's 18 provinces would block the constitution even if most Iraqis backed it. This clause was originally written in by Kurdish negotiators to protect their interests.
Initial estimates have suggested 60% of the 15.5 million Iraqi voters cast their ballots in Saturday's referendum.
Provisional results are expected in two days, with full results three or four days later.
Insurgent violence was sharply curbed during the vote, six Iraqis were killed in various attacks and five US soldiers died in Ramadi, the capital of Al-Anbar province.
Thirty-six people were killed during Iraq's legislative election on 30 January.
Approval of the draft constitution would pave the way for parliamentary elections in December, although the constitution is likely to be quickly amended once a new round of general elections are held.
