The events unfolded in a police lockup in the town of Acarigua on Friday.
"There was an attempted escape and a fight broke out among gangs," the state's public safety secretary, Oscar Valero, told the media. "With police intervention to prevent the escape, well, there were 29 deaths."
Prisoners detonated three grenades, resulting in injuries to 19 police officers, Valero said, reported Efe news.
The lockup in Acarigua holds more than 350 people awaiting trial, he said.
The Venezuelan Prisons Observatory (OVP), an independent advocacy group, said blame for the deaths lay with the Ministry of Penitentiary Services, created eight years ago to address chronic overcrowding, corruption and violence in the nation's 30 prisons.
What happened in Acarigua was a "massacre," OVP said on Twitter.
Another Venezuelan NGO, Una Ventana a la Libertad (Window on Freedom), said the disturbance began on Thursday night with a protest by prisoners demanding transfers to other facilities.
A cell-phone video from inside the lockup showed a masked, gun-wielding inmate with two female visitors.
In March 2018, 66 prisoners and two visitors perished in a fire at a police station lockup in Valencia, Carabobo state.
"We're talking about 68 human beings who died because of irresponsibility, incompetence, ignorance on the part of the government," the general coordinator of OVP, Humberto Prado, said at the time in an interview with the VPI television network.
Attorney General Tarek Saab said that overcrowding played a role in the Valencia tragedy, which reportedly began with a mutiny by inmates in reaction to a search operation. Two police officers were charged with manslaughter in connection with the blaze.
Scores of inmates have died violently inside Venezuela's prisons over the last decade.
Nearly 55,000 people are being held in prisons built to house 35,562 inmates, according to the OVP.
( With inputs from IANS )