Local residents, however, said turnout at the polling stations seemed lower than in previous referendums.
Our correspondent said it was a close-fought race in a "very polarised country".
After casting his vote at a polling station in a Caracas slum, Chavez promised to abide by the outcome.
"We'll recognise the result, whatever it is, once it is announced by the National Electoral Council," he said.
Chavez has previously described winning the vote as key to completing his transformation of Venezuela into a socialist state.
"On Monday I'll wake up looking beyond 2013," Chavez said. "That will give me more confidence in what we're doing ... and greatly diminish political uncertainties."
Popular among the poor
Spearheaded by a student movement, the opposition's campaign slogan is "No is No," referring to Chavez's 2007 effort to push through constitutional changes that would extend his presidency.
Chavez lost that vote, his only electoral defeat in 10 years in office.
"My certainty in victory is infinitely higher than on December 1, 2007," Chavez said.
Chavez is popular with many of the country's poor for health and education programmes, but blamed by a vocal opposition for rising crime, corruption and inflation.
His opponents say a victory for Chavez in the referendum would remove the last remaining check on his power.
Oscar Perez, a representative of the opposition, called Chavez's government "fascist" and "intolerant".
The opposition says Chavez called the vote - which takes place only three months after the opposition gained ground in regional and municipal elections - before the country feels the impact of falling oil prices, the main source of funding for the president's social programmes.
With a strong grasp on the private media, the opposition has focused its campaign on the importance of alternating power for democracy in their campaign, and accused Chavez of abusing state resources to fund a massive "Yes" campaign.
Rob Winder, also reporting for Al Jazeera from Caracas, said both campaigns appeared confident that they can claim victory, but that the "Yes" camp believed more of their supporters were turning out to vote.
He said while groups of young Chavez supporters patrolled the streets on motorcycles, the "No" campaign seemed to have adopted a low-key approach, concentrating instead on monitoring how the vote has been conducted.
About 100 international observers have been accredited to observe the referendum, but neither the Organisation of American States (OAS) nor the European Union have official observers in Venezuela.
Polls conducted at the end of the campaign showed Chavez has a slight lead among those who have already decided.
Two pollsters on Saturday - Datanalisis, which works for the public and private sector, and Consultores 30.11, which works for the government - gave the "Yes" vote a lead of between five points and seven points.
Chavez has been widening his lead slightly since January, the pollsters said.
Both surveys conducted during the final week of the campaign also said more than 10 per cent of Venezuelans who planned to vote still had not made up their minds, making the outcome hard to predict.