A statement from the Holy See said Francis had met Maduro because the pontiff's heart was with the Venezuelan people.
Maduro is accused by the opposition-majority legislature of committing a coup d'etat by blocking a referendum on removing him from power.
“The meeting took place in the context of the worrying situation of political, economic and social crisis which the country is going through and which has had severe repercussions on the daily life of the entire population,” the statement said after the encounter.
“In this way, the pope, who has the wellbeing of all Venezuelans in his heart, wanted to offer his contribution in support of constitutionality in the country and to every step that could help to resolve the open questions and create greater trust between the parties.
“He urged (the parties) to show courage in pursuing the path of sincere and constructive dialogue, to alleviate the suffering of the people, particularly of the poor, and to promote renewed social cohesion, which will allow the nation to look to the future with hope.”
Opposition lawmakers in Venezuela on Sunday passed a resolution declaring “the breakdown of constitutional order” and “a coup d'etat committed by the Nicolas Maduro regime”.
The measure came during an emergency session on the crisis gripping the resource-rich but recession-hit South American state.
Maduro visited the pope on his way back from the Middle East, where he was lobbying for cuts to oil production to help crude prices improve and stem the free-fall of his country's economy.
The heir to Hugo Chavez, socialist Maduro has seen his political support crumble of late with a recent poll finding that 75 percent of Venezuelan voters disapprove of him.