The prosecutors' office said an investigation had been launched into "the deaths of 37 people" in the facility in the town of Puerto Ayacucho.
Governor Liborio Guarulla had earlier tweeted that a "massacre" took place with at least 35 corpses counted.
Prosecutors said 14 officials were wounded in the violence which ran from Tuesday into early yesterday, but did not say if any were among the dead.
Two prison-monitoring groups, A Window to Freedom and the Venezuelan Prisons Observatory, said the 37 killed were all inmates.
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"In this one, detainees are only supposed to be held for up to 48 hours, but there were prisoners who have been there for years," he said.
The jail was holding 105 prisoners at the time of the riot, Guarulla said.
The deadliest riot in a prison in Venezuela was in 2013, when 60 people died and more than 150 were wounded in a facility in Uribana, in the western state of Lara.
At the end of last year, the country had 88,000 detainees, more than double the official holding capacity of 35,000 places, according to A Window to Freedom. So some 33,000 convicted prisoners were being kept in preventative centres like the one in Puerto Ayacucho, alongside people awaiting trial, Nieto said.
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