The voting follows weeks of violent street protests in which many people have been killed or injured. On Sunday the death toll rose sharply with at least six people -- including two teenagers -- killed at protests and a National Guard officer also reported dead by the Attorney General's Office.
The death toll from the unrest ongoing since early April is 125, according to a statement from the Venezuelan attorney general's office. That number does not include at least two of Sunday's deaths, in which the reasons for the killings are under investigation.
Polls were set to close at 7 p.m. ET, after officials extended voting by one hour.
Maduro, in a 2½ minute message posted to Twitter, called the vote a historic moment.
"This has been and is a successful day with great participation," he said. "... Today is a day of victory."
International reaction was harsh, with many nations, including the United States, condemning the election.
Clashes in the streets, call for Monday protest
A key opposition figure, Henrique Capriles, governor of Miranda state, labeled the election fraudulent and called for massive protests a noon on Monday.
Speaking at a press briefing in Caracas, Capriles said voter participation Sunday was less than 15%. He claimed voter turnout was three times higher two weeks ago for an opposition-led, non-binding referendum against Maduro's proposed Constituent Assembly.
In the streets Sunday, National Guardsmen clashed with opposition protesters and police fired tear gas at crowds in Caracas. As dozens of police officers rode motorcycles through the Altamira neighborhood, a large explosion went off. Agence France-Presse video showed two officers, each with a leg on fire as comrades rushed to help them.
At one spot in the capital, opposition demonstrators set up barricades on a highway.
News broke early that one of the candidates in the election, lawyer José Félix Pineda, had been shot dead in his home on Saturday and that opposition leader Ricardo Campos died Sunday morning.
The attorney general's office tweeted that a state prosecutor is investigating Pineda's death.
"A group of people broke into the home of the victim in the Brisas del Sur sector and shot him multiple times," the attorney general's office said in a tweet. Pineda is listed as candidate number 3 in Bolivar state.
A state prosecutor also is investigating the death of Campos, youth secretary for Accion Democratica, an opposition group. He died in Cumana, a coastal town 250 miles east of Caracas. The circumstances of his death have not been disclosed.
Young Venezuelans have taken to the streets
for months to protest the vote, known locally as "la constituyente," or the constituent. The Venezuelan National Guard and protesters clash nearly every day.
The polls opened at 6 a.m. ET Sunday, with nearly 380,000 troops guarding voting stations, according to a government release. Many cast their ballots in support of the government's initiative.
Elio Herrera, who voted early in a Caracas neighborhood, called the exercise "democratic and popular."
"It was a quick and simple process," Herrera said, describing the ambiance at the polling station as happy and hopeful.
Protest banned by government
Experts have said the outcome is a foregone conclusion: Maduro will be able to consolidate political power. The opposition to Maduro fears the vote will erode democracy and give the Venezuelan leader sweeping authority.
Maduro's administration has deemed any protests illegal, threatening anyone who defies the no-protest order with up to 10 years in prison.
Maduro, who said he was the first voter in Sunday's election, called casting the first vote a symbol of the independence and sovereignty of Venezuela.
He accused US President Donald Trump of trying to "prevent the people from carrying out its right to vote," and boasted that his government is seeing through the vote despite international pressure.
"The Constituent Assembly will be the space, the power of powers, the superpower that will, so to speak, recover the national spirit, find reconciliation, justice, find the truth."
Maduro's opponents control the National Assembly, holding 112 of the body's 167 seats, and have been battling with him for political power since they won a majority of seats
in December 2015. Before the winners of those elections took office, Maduro stacked the country's Supreme Court with loyalists to prevent his own impeachment.
The proposed Constituent Assembly would be made up of 545 members, all nominated by Maduro's administration. Nominees include his wife, Cilia Flores, and prominent loyalists such as former Foreign Minister Delcy Rodriguez and former Vice President Diosdado Cabello.
The opposition hasn't submitted any candidates for the vote because it doesn't recognize the legitimacy of the election. Ultimately, the vote and the creation of Maduro's Constituent Assembly would give the President immense political power.
Maduro says the vote will help bring peace to a polarized country, with all branches of the government falling under the political movement founded by Maduro's late mentor and predecessor, Hugo Chavez.
Critics in Venezuela and abroad argue a Maduro mandate would erode any last signs of democracy in the country. "It would give the government the opportunity to turn Venezuela into a one-party state without any of the trappings of democracy," says Eric Farnsworth, vice president of the Council of the Americas, a business association.
Trump recently said
in a statement that Maduro "dreams of being a dictator." His administration sanctioned 13 Venezuelan leaders
associated with Maduro this week.
On Sunday, the US State Department issued a statement condemning the vote: "The United States stands by the people of Venezuela, and their constitutional representatives, in their quest to restore their country to a full and prosperous democracy. We will continue to take strong and swift actions against the architects of authoritarianism in Venezuela, including those who participate in the National Constituent Assembly as a result of today's flawed election."
Mexico, Colombia and Panama followed with sanctions of their own against the same individuals. Argentina and Mexico said they won't recognize Sunday's vote results. Canada denounced the vote.
The Organization of American States deems the vote illegal. Spain said it will study, along with its partners in the European Union and countries friendly to the region, additional measures that may be effective in promoting a restoration of democratic institutions.
Nicaragua came to Venezuela's defense, praising it for the "historic day for the brave people of Bolívar y Chávez, the President Nicolás, the United Socialist Party."
Trump warned he would take further "strong and swift economic action" against Maduro after the vote, though his administration hasn't elaborated beyond saying all options are on the table.
Venezuela's ministry of communication did not respond to CNN's request for comment on the vote.
On July 16, more than 7 million Venezuelans cast ballots
in an unofficial vote against Maduro's Constituent Assembly. Maduro ignored the results of the vote, which was organized by opposition leaders.