About a third of voters had cast their ballots by mid-morning, according to the government. With the main opposition boycotting the vote, President Nicolas Maduro is expected to win.
Venezuelans went to vote in a presidential election on Sunday as the country struggles with a deepening economic crisis.
President Nicolas Maduro is expected to win another term in power, with the main opposition boycotting proceedings they describe as a "farce."
In a pro-government area of the capital, Caracas, election workers said less than a fifth of the 1,916 voters had turned out by mid-morning but said they expected a surge at mid-day.
The US Deputy Secretary of State John Sullivan said on Sunday the US would not recognize the result of the vote which is to be discussed at a meeting of the G20 in Argentina on Monday. "We need to make sure we adhere to our goal which is to target corrupt regime officials and not the people of Venezuela," Sullivan said.
In the running
'Power to act'
Maduro has blamed the United States and a criminal mafia within the country for Venezuela's economic struggles. "If you don't go to vote, you will be taking away from me the power to act against the criminal mafia of the economy; against the mafia of the illegal commerce and to do all what I want to do with the power that you have to give to me," he said as campaigning drew to a close.
Falcon, whose challenge has drawn small crowds and little media coverage, has said he wants to free Venezuela from dictatorship. "Our administration will be one that respects human rights and we'll achieve this by voting, not by boycotting. Here we have the response to the boycott, the people's response which says, 'we're not going to sit with our arms folded' because we have to go out and defend Venezuela."
Juan Pablo Guanipa, of the main opposition coalition, has condemned the vote and Falcon's participation. "These are not elections. They are a farce intended to keep Maduro in power without popular support."
The election has been denounced as undemocratic by the United States, 14 Latin American countries and the European Union.
Maduro is accused of undermining democracy, usurping the opposition-dominated parliament and replacing it with an all-powerful Constituent Assembly.
The president already enjoys a tight grip on the country's military and electoral authorities.
The oil-producing country's economy is in steep decline, being set to contract by 15 percent by the end of this year.
Broadcasters have been forced to close as their licenses have expired without being renewed. Meanwhile, many newspapers have been forced to close due to a lack of paper, the distribution of which is managed by a government-controlled company.
rc/jlw (Reuters, AP, AFP, dpa, EFE)