Opposition leaders hailed it as a success, while also mourning the death of one woman killed by gunmen in Caracas during the voting.
In concluding the Angelus prayer this Sunday at the Vatican, Pope Francis said he is keeping the people of Venezuela in his prayers. Opposition leaders said that was because it was only able to set up 2,000 polling places in a largely symbolic exercise that the government labeled as illegitimate.
At the beginning of June, Pope Francis said: "my voice resonates in that of the Venezuelan bishops". "But these 7 million people spoke and it was plenty".
Now, opposition leaders are promising "Zero Hour" in Venezuela to demand a general election and stop the leftist Maduro's plan to create a controversial new legislative super-body called a Constituent Assembly in a July 30 vote.
Canada and Mexico were among the countries that issued statements Sunday evening lauding the opposition vote.
"Overall the package is pretty radical, especially the idea of a parallel government", said David Smilde, a Tulane University expert on Venezuela.More news: Martin Landau Dies, Aged 89
Five former Latin American presidents - from Bolivia, Colombia, Mexico and two from Costa Rica - were also in Venezuela at the invitation of the opposition to observe the vote. Moncada offered no evidence to support his accusations.
The opposition blamed the attack on "paramilitary groups" linked to the government.
Video posted to social media showed huge crowds outside the church before running in panic as men on motorbikes zoomed past and shots rang out.
He said: "I'm calling on the opposition to return to peace, to respect for the constitution, to sit and talk".
The opposition also said the country's National Assembly, which it controls, would name new members to the government-dominated Supreme Court, setting up a showdown with President Nicolas Maduro, whose party controls almost all other state institutions.
But she said it's falling apart in the hands of the government. "Today we're following his legacy, with President Nicolas Maduro ..."More news: No direct involvement of Pak Army in JIT investigation: ISPR
They said they're voting to recover democracy in their country.
Still, Maduro has vowed that Sunday's referendum will do nothing to stall a July 30 election for delegates for a constituent assembly, which will be responsible for rewriting the country's 18-year-old constitution.
"There's kids dying because they are starving, there's no food, there's no medicine", Cabrera said. "There's no separation of powers, no freedom of expression".
The Venezuelans who participated in the plebiscite answered three questions. Do they reject the constitutional assembly?
"One particular thing that makes this act unlawful is that they never consulted with the people if they people want to change the constitution". However the vote, dismissed by Mr Maduro as illegal, was largely boycotted by government supporters. The government blames the crisis on an economic war waged by its opponents and outside backers.
In early July, armed pro-government militias supporting Venezuela's controversial President Nicolas Maduro stormed the country's Parliament, and assaulted several opposition deputies amid the ongoing anti-government protests in the South American country.More news: Caitlyn Jenner slams Rob Kardashian for posting revenge porn