Lucena said the election process for the National Constituent Assembly is audited by local and worldwide entities, and that her organization will ensure and protect the Venezuelan people's right to vote, despite recent threats by the opposition to stage violent protests and prevent the election.
An Associated Press reporter toured more than two dozen polling places in neighborhoods across the capital, including many traditional strongholds of the ruling socialist party in southern and western Caracas. Many people have been stocking up food and staying home. All the others had at most a couple of dozen voters, and many had less than a half-dozen or were completely empty.
He also called for the "unconditional release of all political prisoners in Venezuela, free and fair elections, restoration of the National Assembly, and respect for human rights in Venezuela", a statement from his office said. "And I think this is just going to make things worse".
While some barricades have been set up in opposition-friendly eastern Caracas, the large crowds seen during previous demonstrations that have drawn hundreds of thousands are largely absent. At least three police were wounded when one of their motorcycles detonated in a powerful explosion. President Donald Trump has warned of "strong and swift economic actions" if Maduro proceeds with his plans.
The run-up to the vote has been marked by months of violent clashes between protesters and the government.
Maduro said: 'We've stoically withstood the terrorist, criminal violence. "Hopefully the world will respectfully extend its arms toward our country".
Amid government fears of low turnout, Venezuela's 2.8 million state employees were under huge pressure to vote, including threats of dismissal.
Accompanied by state media and close advisors, Maduro voted at 6.05am local time - far earlier and less publicly than in previous elections.
"I'm here because I'm hoping for housing", said Luisa Marquez, a 46-year-old hairdresser. "The people are not going to give up the streets until this bad government goes", one 54-year-old militant, Carlos Zambrano, told AFP. "Those who are attacking us to kill us with hunger and blame the government are the same enemies the government's always had".
Most of the Organization of American States has condemned the vote, with several countries saying they wouldn't recognize the results.
The Swiss Foreign ministry has said it is "deeply concerned" about the current situation in Venezuela and that the election of a new constituent assembly in the country should be scrapped.
Maduro said the new legislature - called the Constituent Assembly - "will be the space, the power of powers, the super power that will, so to speak, recover the national spirit, find reconciliation, justice, find the truth".
Congress has already been severely weakened by the Maduro-loyalist electoral commission and supreme court.
The election, and opposition rejection of it, has heightened the sense of alarm among Venezuela's citizens, who are finding it increasingly hard to survive among food shortages and runaway inflation.