Al-Ja'fari told Radio Free Iraq that he hopes Iraqis will approve the referendum, and demonstrate they are "heroes."
"My message to the Iraqi people is that, God willing, today Iraqis will emerge as heroes, that with courage and awareness they will say their 'yes,' confident of the future and in their own free will," he said. "They will not only vote for the constitution but will continue to display such excellent awareness and high confidence to translate the constitution into reality."
Iraqi police and soldiers are guarding more than 6,000 polling stations across the country, with U.S. and other foreign troops ready to assist in case of insurgent attacks.
Security appears to be holding, although a roadside bomb northeast of Baghdad has killed three Iraqi soldiers and there are reports of gun battles in the western city of Al-Ramadi and other locations.
The charter will be ratified if more than 50 percent of voters approve it, and as long as two-thirds of voters in any three of Iraq's 18 provinces do not vote against it.
Initial results may arrive as early as late today. Full results are not expected before 17 October.
Polls are expected to close at 1400 UTC.
(Radio Free Iraq, news agencies)
For RFE/RL's full coverage of Iraq's constitutional referendum, see "Iraq Votes 2005"