The referendum result strongly backed opposition to the socialist government’s proposed constitutional changes.
Venezuela remains polarized between supporters of President Nicolas Maduro and the opposition, which wants fresh elections.
A 61-year-old woman was shot dead while queuing to vote in the capital, Caracas.
Men on motorbikes opened fire, killing Xiomara Soledad Scott, and wounding three others.
The opposition blamed a “paramilitary” gang for the shooting, which prosecutors said they would investigate.
Separately, journalist Luis Olavarrieta was kidnapped, robbed and beaten by a group, but managed to escape.
More than 100 people have died in clashes and protests in Venezuela since April.
Cecilia García Arocha, the rector of the Central University of Venezuela, said 6,492,381 people voted within the country and another 693,789 at polling stations abroad. However, the vote has no legal status.
The turnout is slightly less than the 7.7 million people who voted for opposition candidates at the 2015 parliamentary elections. There are 19.5 million registered voters in Venezuela.
Voting Yes or No to three questions, 98% rejected the new assembly proposed by President Nicolas Maduro and backed a call for elections before his term of office ends in 2019.
They also voted for the armed forces to defend the current constitution.
An official vote will be held on July 30 for a new assembly, which would have the power to rewrite the constitution and to dissolve state institutions. However, critics say the new assembly could herald dictatorship.
The July 16 unofficial poll was held in improvised polling stations at theaters, sports grounds and roundabouts within Venezuela and in more than 100 countries around the world.
However, President Maduro described the vote as “meaningless”.
“They have convened an internal consultation with the opposition parties, with their own mechanisms, without electoral rulebooks, without prior verification, without further verification. As if they are autonomous and decide on their own,” he said.
Nicolas Maduro argues that the constituent assembly is the only way to help Venezuela out of its economic and political crisis.
Opposition leaders fear that the process of setting up a new constituent assembly and rewriting the constitution would almost certainly delay this year’s regional elections and the 2018 presidential election.
They also fear that the constituent assembly would further weaken the National Assembly, Venezuela’s opposition-controlled legislative body.
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