In the capital Astana, Nazarbaev said after casting his ballot that this year's election is being held in "unprecedented democratic conditions."
However, opposition candidate Zharmakhan Tuyakbai told RFE/RL in the southeastern city of Almaty that there had been early signs of fraud. "Since early morning, we have received information from different regions that there have been many irregularities during voting and attempts to rig the elections," he said.
Another opposition challenger, Alikhan Baimenov, also said he had information about irregularities coming from polling stations in the regions.
The Central Election Commission said nearly 70 percent of eligible voters had cast their ballots two hours before the polls closed.
Early results are expected on 5 December.
(with news agencies)
Workers at Almaty polling station No. 310 registering election monitors prior to the opening of voting on December 4