Sanders told The Associated Press that the meeting took place before the pope left for his one-day visit to Greece.
He said he was honored by the meeting, and that he told the pope he appreciated the message that he is sending the world about the need to inject morality and justice into the world economy.
Sanders said it's a message he has been sending as well.
"We had an opportunity to meet with him this morning," Sanders said. "It was a real honor for me, for my wife and I to spend some time with him. I think he is one of the extraordinary figures not only in the world today but in modern world history."
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Clinton holds a 250-delegate lead over Sanders in the primaries and the senator is trying to string together a series of victories in upcoming contests to draw closer to the nomination.
Sanders said it was a brief meeting at the papal residence. "I told him that I was incredibly appreciative of the incredible role that he is playing in this planet in discussing issues about the need for an economy based on morality, not greed."
Dr Jeffrey Sachs, a Sanders foreign policy adviser and adviser to the United Nations on climate change, said there were no photographs taken of the meeting.
The Vatican is loathe to get involved in electoral campaigns, and usually tries to avoid any perception of partisanship as far as the pope is concerned.
Popes rarely travel to countries during the thick of political campaigns, knowing a papal photo op with the sitting head of state can be exploited for political ends.
"His message is resonating with every religion on earth with people who have no religion and it is a message that says we have got to inject morality and justice into the global economy," Sanders said.