The General Penitentiary of Venezuela in central Guarico state was closed in October after violent clashes between inmates.
The bodies, which are in an advanced state of decomposition, were found during works to refurbish the jail.
So far none of the remains have been identified.
The grave was discovered on Thursday and the number of bodies found since has risen from seven to 14.
Forensic experts are continuing with their search and have not ruled out finding more bodies buried on the prison grounds.
On Friday, prison minister Iris Varela wrote on Twitter that she had contacted the relatives of two inmates to ask for their help identifying the remains.
The two prisoners disappeared when inmates were relocated from the General Penitentiary of Venezuela to other jails in October.
An estimated 9,000 prisoners were locked up in the jail near the town of San Juan de los Morros prior to its closure, according to non-governmental organisation A Window on Freedom.
The NGO says Venezuelan jails are woefully overcrowded and that last year 173 inmates died while in custody.
But Ms Varela told Venezuelan state broadcaster VTV that the country had taken huge steps to improve the conditions of its prisons.
She said that all of the country's women's and youth prisons had been brought up to new standards set by the Venezuelan government.
"This is an achievement without precedent of the Bolivarian Revolution and the government of our president, Nicolas Maduro," she said.
She said that President Maduro had asked her in 2014 to "impose maximum discipline" in Venezuelan jails.
"Well, here I am fulfilling the president's orders," she said.
She did not refer further to the remains found except to say that forensic tests were being carried out.

Santa Cruz defeated Frampton in a Vegas rematch to reclaim the title he lost in New York last year, but has dampened talk of a third meeting in Belfast.
"I think more likely first I would like to unify with Lee Selby," he said.
"Selby is calling me out, so I want to make it with him and get the win and then fight [Abner] Mares or Frampton."
Selby's camp say they will discuss the prospect with Al Haymon, who advises both fighters, and that a fight with the Mexican would be their "first choice".
The Barry boxer stopped Spain's Andoni Gago on the undercard of the Tony Bellew v David Haye bill at the O2 Arena on Saturday and has made clear he is now a free agent after his four-year agreement with Matchroom concluded.
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"We will discuss options with Al Haymon this week," Selby's manager Jamie Sanigar told BBC Wales Sport.
"We want the biggest fights now and a unification with Santa Cruz is top of the list. The winner of Selby v Santa Cruz would be king of the castle in the featherweight division."
Selby is supposed to fight mandatory challenger Jonathan Victor Barros next after their previous fight was cancelled at the last minute.
A unification fight with Santa Cruz could well be an attractive proposition to both organisations, though the IBF says it has heard nothing on a potential unification duel and expect Selby's camp to negotiate with Barros.
"Selby and Barros have been ordered to negotiate again.  They have until 2 April," the IBF told BBC Wales Sport.
"We have not been approached about a unification and [Selby] will likely have to fight Barros prior to a unification with Santa Cruz."
The IBF says Barros' issues that led to their previous fight being postponed have been resolved.
The Nevada Athletic Commission did not give an explanation other than the Argentine had not met its requirements.
Santa Cruz believes a unification fight with Selby would be the preferable option.
"I want to fight the best. There is Lee Selby, I want to unify against him, Abner Mares, Carl Frampton, I will fight any of them," Santa Cruz confirmed.
"But I think more likely first I would like to unify with Lee Selby,  I don't know about a date yet, but maybe June, July, or August. We will talk about it."
The number of bodies found in a mass grave in Venezuela's largest prison has risen to 14, the public prosecutor's office said in a statement.
[NEXT_CONCEPT]
WBA featherweight champion Leo Santa Cruz says he wants a unification fight with IBF champion Lee Selby before facing Carl Frampton again.