(CNN) The leader of the Roman Catholic Church and the President of Iran met Tuesday at the Vatican, a face-to-face encounter that speaks to a changing geopolitical landscape and both men's significant role in it.

Cameras captured Pope Francis and President Hassan Rouhani shaking hands and sitting down across from each other. The Vatican later offered a glimpse into what it called"cordial discussions" touching on the Islamic Republic of Iran's nuclear accord and "problems afflicting the Middle East."

While the Vatican news release didn't mention any specific group or country, no doubt the agenda included talk about the years-long war and humanitarian crisis in Syria and Christians endangered by Islamist extremists such as ISIS in that country, neighboring Iraq and elsewhere.

"The parties highlighted the importance of inter-religious dialogue and the responsibility of religious communities in promoting reconciliation, tolerance and peace," the Vatican said.

The pair -- one a Muslim cleric, the other the world's most recognized Christian leader -- had planned to sit down in November, according to official Iranian and Vatican news outlets. But Rouhani postponed that meeting, and his entire trip to Europe , following that month's coordinated terrorist massacre in Paris.

They entered Tuesday's talks with high expectations at a time when Iran's role in global affairs has evolved considerably.

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Just last fall, Tehran was still subject to widespread sanctions over its nuclear program. Those sanctions have recently been lifted as part of a deal that Rouhani championed, arguing since his 2013 election that it's in his nation's best interest to resolve the issue and become more involved in world economic and political affairs.

Prior to the sitdown, Italian Foreign Minister Paolo Gentiloni told CNN's Christiane Amanpour, "I think that the meeting of President Rouhani with the Pope is one of the signals of the fact that, after the nuclear deal, we have a possibility of a relevant involvement of Iran in a regional and global framework."

Syria war likely high on the agenda

Economics played a big part in Rouhani's push for a nuclear accord, and in his European trip. To that end, before the Vatican meeting, Italian and Iranian officials signed billions of dollars in trade deals that Gentiloni says mark "a new era in economic relations."

It's highly unlikely, though, that business matters were high on the agenda for Pope Francis. Yet the Catholic leader has been a top worldwide figure on many issues -- leadership that led Time magazine to name him its 2013 Person of the Year -- that would be relevant in a sit-down with Rouhani, Syria likely foremost among them.

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Francis has persistently called for peace and opposed widening military interventions in Syria, even making the message a focus of his first Christmas as Pope . In response, and in apparent recognition of the Pope's high moral standing worldwide, embattled Syrian President Bashar al-Assad sent a message of appreciation for Francis' words and his support for a peaceful resolution "through national dialogue."

Yet little has changed since then in Syria. If anything, things seem to have gotten worse. U.N. envoy Staffan de Mistura said this month that the war has left more than 220,000 people dead, 1 million wounded, 3.3 million as refugees, 7.6 million internally displaced and 12 million total in need.

Iran has been one of Assad's few allies, though it's largely been on the sidelines in international efforts to broker some sort of peace. Increasing openness to Tehran may mean a new role for Rouhani and other officials and perhaps contribute to a breakthrough.

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The latest round of Syria peace talks were set to begin Monday in Geneva, Switzerland, only to be delayed due to ongoing discussions about who should represent the Syrian opposition, de Mistura said. Both U.S. Secretary of State John Kerry and his Russian counterpart, Sergey Lavrov, have publicly urged talks as soon as possible -- though the fact there's not even agreement on who should talk speaks to how complex, convoluted and emotionally charged this conflict is.

Gentiloni, the Italian foreign minister, expressed hope that Iran's increasing engagement could be pivotal in what happens in Syria.

"I think that diplomacy made a little miracle with the nuclear deal," he said. "We need, now, perhaps a second one ... I think that Iran should be involved."

'Common spiritual values emerged'

Islam is not only the official religion in Iran, it's fundamental to its existence under supreme leader Ayatollah Ali Khamenei. The CIA World Factbook reports that 99.4% of Iran's roughly 81 million people are Muslim, the vast majority of them (90 to 95%) being Shiites like Khamenei and Rouhani.

Francis himself also has been outspoken in calling for mutual respect with Muslims and promoting dialogue between various religions. And the Vatican -- the official home of the Roman Catholic Church -- has been tied to Iran in the past.

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Gentiloni noted that predominately Catholic Italy, where the Vatican is based, has had relations with Iran for centuries. And more recently in 1999, then-Iranian President Mohammad Khatami met with Pope John Paul II and, six years later, was among the scores of world leaders attending the pontiff's funeral.

"I wish this day could be a moment that makes us hope for a future of peace, not of conflict and hostility," the Iranian President said on that day, as reported by the Catholic News Service

The Vatican played up the commonalities on Tuesday, while also referencing "the life of the Church in" Iran and "the promotion of the dignity of the human person and religious freedom."

In its statement on the Francis-Rouhani talks specifically, the Vatican said, "Common spiritual values emerged, and reference was made to the good state of relations between the Holy See and the Islamic Republic of Iran."