The crisis has seen the popularity of Maduro's government collapse as opposition parties call for snap elections, but he has refused to give up power.
The political deadlock promises little respite for those suffering in the listing economy of the oil-rich South American nation.
Maduro has rejected calls fora new presidential election before the scheduled 2018 vote. "We have given an indisputable mandate for a new Venezuela starting tomorrow". Opposition leaders said that was because it was only able to set up 2,000 polling stations.
The president urged the opposition to "come over to peace, to the constitution", telling officials who were setting up his July 30 election that differences "must be resolved in peace, with ballots, not bullets".
Venezuelans across the world and here in the Valley gathered to vote in an unofficial election.
Opposition leaders hailed it as a success, while also mourning the death of one woman killed by gunmen in Caracas during the voting.
Colombia's former President Andres Pastrana, left, embraces Lilian Tintori, left after a news conference of worldwide observers of a symbolic referendum in Caracas, Venezuela, Sunday, July 16, 2017.
Most Venezuelans oppose the Constituent Assembly, which will have power to rewrite the constitution and annul the current opposition-led legislature, but Maduro is pressing on anyway for the vote in two weeks' time.
Maduro has called for the creation of a "constituent assembly", a Soviet-like body that will seek to modify the country's constitution.
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Meanwhile, the opposition praised the vote as proof that Venezuelans demand democratic change.
"Overall the package is pretty radical, especially the idea of a parallel government", said David Smilde, a Tulane University expert on Venezuela.
State media largely ignored Sunday's event, concentrating instead on a simultaneous, government-organised practice run for the July 30 vote.
Men on motorbikes opened fire, killing 61-year-old Xiomara Soledad Scott, and wounding three others.
But she said it's falling apart in the hands of the government. The Venezuelan government has responded with lethal force, killing more than 90 citizens in clashes with protesters.
In the wake of Nicolas Maduro succeeding former socialist president Hugo Chavez after the latter died from cancer in 2013, the country has been marred by violence and social upheaval. The court nullified eight of the assembly's laws between January and October 2016, after making just one such ruling in the previous 200 years, legal experts say.
"This is really important because I think it's the first step in recovering our country because it's really bad right now", Claudia Cabrera, a local Venezuelan resident, said. The people expressed themselves and told the Executive what they want: they want peace. Do they support the formation of a government comprised both of Maduro backers and opponents?
Venezuela has been plagued by daily outbursts of anger over food shortages and an economic crisis characterised by rampant inflation.
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