Centres where voters were still in line would stay open until voting was over, following electoral law, Lucena said.
Maria Teresa Padron, 80, from the vast Petare slum in Caracas, voted for a candidate from Chavez's party to show her support for the president.
"God sent us Chavez. No one will give us the well-being this president offers us. No one took us into account before, but thanks to him, I live well now," she said.
Another resident, Cesar Alberto, chose an opposition candidate for a municipal post to protest against the current mayor.
"The president came to support his candidates but not to see the problems here. There's rubbish, violence and a lack of water," he said, pointing to piles of trash.
Chavez remains the country's most popular politician and enjoys overwhelming control of local offices.
But he faces an opposition buoyed by last year's defeat of his attempt to abolish term limits and by growing discontent over crime, corruption and inflation that have blighted his socialist ambitions.
Chavez himself says these elections for governors and mayors could decide "the future of the revolution, the future of socialism and also the future of Hugo Chavez".
A setback could force Chavez to contend with hostile local-level opponents with revived national clout. Victory would help him lay the groundwork to extend his rule beyond 2013, when his six-year term ends.
|Pre-election polls showed Chavez's candidates leading in a majority of races [AFP]
Pre-election polls showed Chavez's candidates leading in a majority of races, while the opposition was ahead or in tight races in several of Venezuela's most populous states.
Teresa Bo, Al Jazeera's correspondent in the capital, Caracas, said: "Everyone is wondering how strong the oppositon is.
"Chavez feels very popular and people continue to love him. His approval rating is around 60 per cent. The big question is not how many states he'll win, but how many he will lose."
Chavez already has a congress filled with supporters and a Supreme Court that critics say is in his pocket as he tries to hold on to power in state houses and city halls.
Chavez has threatened to cut off national funds to states that end up in the hands of opponents. He also has warned he might need to send tanks to defend his government if an opponent wins in the hard-fought Carabobo state.
Candidates include Chavez's older brother Adan, who was in a tight race to succeed their father as governor of Barinas, Chavez's home state. Chavez's ex-wife Marisabel Rodriguez was also on the ballot - on the opposition side.
|Chavez's older brother was in a tight race to succeed their father in their home state [AFP]
Rodriguez, running for district mayor in her hometown, Barquisimeto, said her campaign may have been local but it was also "against the danger posed to democracy by leaving a single person in power for a long time."
Chavez's allies swept the last state elections in 2004, winning all but two of 23 governorships and a majority of local offices. This time, candidates are competing for 22 governorships, 330 mayoral posts and other offices.
Chavez's popularity has rebounded since he suffered his only electoral defeat in 2007 in a referendum that would have allowed him to seek re-election indefinitely.