Hassan Rouhani made the first state visit to Europe by an Iranian president in almost two decades this week, following the lifting of sanctions against his country.
The talks "delved into the conclusion and application of the nuclear accord, and the important role that Iran is called upon to play, together with other countries of the region, was highlighted," the Holy See said.
It added that that role should "foster adequate political solutions to the issues plaguing the Middle East, fighting the spread of terrorism and arms trafficking."
The "cordial" talks also stressed common spiritual values, the statement said.
The Vatican meeting was a key part of the Iranian effort to take a more prominent place on the world stage after the nuclear deal with Western powers.
Iran, which agreed to limit its nuclear activities in exchange for an end to economic sanctions, is eager to carve out a bigger role in mediating Middle East conflicts. Francis' papacy has emphasized mediation and conflict-resolution, including his role in helping Cuba and the United States to normalize their relations.
Francis gave Rouhani a medal depicting St. Martin giving his cloak to a poor man in the cold, describing the saint's act as "a sign of unsolicited brotherhood."
Rouhani brought a gift of a hand-made rug that he said was made in the Iranian holy city of Qom.
Before going to the Vatican, Rouhani told a forum of business leaders in Rome that "Iran is the safest and most stable country of the entire region."
Italy also sees Iran as a potential peacemaker in Syria's civil war, as the Italian government fears the warfare will further destabilize Libya — just across the Mediterranean from southern Italy — fuel terrorism and jeopardize energy security.
"Italy has always backed the role of Iran as a regional player in resolving tensions in the area, starting with the Syrian crisis," Foreign Minister Paolo Gentiloni said after meeting his Iranian counterpart, according to his office.Rouhani has described the political talks leading to the nuclear deal as a potential blueprint for pursuing peace in the Middle East.