"At this time, we are voting with great calm. We have no reports of major disturbances, nor of bad news of attempts to disrupt (the poll)," Tibisay Lucena, president of the National Electoral Council (CNE), told state-run VTV by phone.
The polls opened at 6:00 a.m. local time (1030 GMT) for voters to choose the members of a National Constituent Assembly (ANC) to debate and amend the Constitution, an initiative proposed by the government of President Nicolas Maduro and rejected by the opposition.
In an attempt to encourage voters to go to the polls, Maduro headed to a local voting station early so he could be the first to cast a vote, according to the Caracas-based news network Telesur.
"In an unprecedented move, the Venezuelan president was the first to exercise his right to vote" at 6:05 a.m. local time (1035 GMT), the network said on its website.
"I want mine to be the first vote...the first vote for peace, the first vote for Venezuela's sovereignty and independence, the first vote for the peaceful future of Venezuela," Maduro said.
"Here we are, a peaceful country exercising its right to vote," he added.
His wife and ANC candidate Cilia Flores was the second Venezuelan to cast a vote.
The opposition stepped up protests in the lead up to Sunday's vote, but an announced ban on demonstrations appeared to be keeping things calm.
However, the Public Ministry (MP) said that a candidate for the assembly was assassinated on Saturday night.
Jose Felix Pineda, 39, a lawyer running to represent the southern state of Bolivar, was killed after "a group of people broke into the victim's home...and shot him several times," the MP said via Twitter.
Pineda became the second ANC candidate to have been killed, following the death of Jose Luis Rivas on July 10, in northern Aragua state, also by gunshots.
The ANC was proposed by Maduro on May 1, with a view to reviewing and rewriting the 1999 Constitution to break the current political gridlock that has paralyzed the country. A popular referendum will be held on the new constitution after it is drafted.
According to the constitution, the ANC will act as the supreme organ of power before the new constitution is approved.
The government said that the new constitution would "guarantee peace and coexistence among all Venezuelans," but the leading opposition coalition, known by its Spanish acronym MUD, has refused to take part in the process.
Among the 545 seats of the assembly, 364 will represent regions while 181 represent different civil society groups. About 6,120 candidates are competing for the seats, according to the CNE.
