The regime is known to have committed gross abuses, including violence, against those who don't share their political ideologies, and are accused of taking many political prisoners.
Archbishop Padrón said that for the bishops, their "Magna Carta" on how to move forward in the crisis is the letter Vatican Secretary of State Cardinal Pietro Parolin sent them in December, in which he indicated the conditions under which dialogue with the Maduro regime ought to be carried out.
The four conditions listed by Cardinal Parolin are: the assurance of a humanitarian corridor for food and medicine; respect for and the re-establishment of the National Assembly; the release of political prisoners; and the guarantee of elections.
While Venezuelans had been protesting many of Maduro's moves for some time, the final straw for many was when in late March the president announced his decision to call a constitutional assembly and and to revoke the power of the National Assembly, which had been in the hands of the opposition since 2015.
Part of Maduro's guarantee was that after the constitutional assembly takes place July 30, elections will finally be held in December.
However, Archbishop Padrón said he doesn't have faith in the regime, and believes the deal is "a trap" for the people, because during the July assembly "you can easily vote to annul or not the elections in December. So the December date is just an imaginary figure for the people."
But even though they have very real problems with Maduro, Archbishop Padrón said this doesn't mean that the bishops are on the side of the opposition.
"We don't represent any party, and we don't want to be on the side of the government or the opposition," he said. "We want to help the people."
The bishops came "to present to the Holy Father the situation of the Venezuelan people, whether they are those people who are close to the government, or those who feel far from the government. We don't have any preference in this sense."
During the meeting, the prelates gave the Pope two dossiers, the first containing a list of some 70 people, mostly youth, who have been killed during protests in Caracas and other cities throughout Venezuela. The second document was a detailed outline of the work the bishops conference has done so far to help alleviate the crisis.
After meeting with the Pope, who gave the bishops his "full support" and "total confidence" in their efforts, the six prelates present for the encounter then met with Cardinal Parolin, who before becoming Secretary of State was the apostolic nuncio to Venezuela for four years.
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They later met with officials of the Vatican's charitable organization Caritas Internationalis, which is offering concrete support to needy families on the ground in Venezuela.
Pope Francis specifically told the bishops to "reinforce" the work that Caritas does, not only for the Venezuela branch, but the international organization as a whole, because they are "ready to help" in acquiring and distributing food and mostly medicines to the people.
However, the bishops conference still faces issues when it comes to getting medicines to the people, Archbishop Padrón said. Even though the government technically gave them permission to distribute medication a few weeks ago, the conditions outlined in the fine print make it nearly impossible to do.
The government does this, he said, because they don't want to appear "insensitive" or as "a needy country."
"The international image of the government must be maintained," he observed.