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In a sense, Pope Francis made clear his world views when he wore practical black shoes and a simple black wristwatch to mass – a decidedly more humble look than his predecessor, who sported red leather shoes and a ruby cross.

Then he rocked Twitter when, as @Pontifex, he declared: “My thoughts turn to all who are unemployed, often as a result of a self-centered mindset bent on profit at any cost.”

Pope Francis, who became pope in 2013, has since made other comments on world economic issues, citing the pitfalls of capitalism, decrying global income inequality and equating low-wage labor to a form of "slavery."

He's even described the financial corruption in the church as a "spiritual sickness."

Analysts say Pope Francis—leader of some 1.2 billion Catholics—is not necessarily calling for the demise of free market theory. Rather, he's issuing a strong warning to economic leaders.

"Like many people, he thinks capitalism won't survive unless it decreases income disparity," said George Haley, professor of marketing and international business at the University of New Haven.

"I think it's fair to say he's arguing for a more European version of capitalism going forward, especially after the Great Recession, so there's more of a safety net for people when they need it," Haley said.

Joseph Pastore, a business professor at Pace University believes the pope is focused on equality and justice in economics.

"I don't think he's attacking capitalism or the wealthy, because if he did, that strategy would fail," Pastore said.

(Read more: Pope urges Brazil's youth to fight corruption, apathy)

Some in the business community have taken notice.

"His comments are of high importance to me," said RohitArora, CEO of Biz2Credit, an online site that connects small-business owners with financing. "The kind of issues he's talking about are too often ignored by religious and business leaders."

Although surprising, the pope's comments on global economics are in line with his beliefs, said Mathew Schmalz, a professor of religious studies at the College of the Holy Cross.

"Being a Jesuit priest and having spent so much time in Argentina as bishop and cardinal had a great effect on him," Schmalz said. "He's seen a lot of poverty close up and raised the issue in Argentina before becoming pope."

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Papal statements on social and economic justice are not new. In the past century or so, popes have made their thoughts on the issues known through open letters—what the church calls encyclicals.

In 1891, Pope Leo XIII issued an encyclical that rejected both communism and unrestricted capitalism, while affirming the right to private property. But he also supported the rights of labor to form unions, and the need for some "amelioration of the misery and wretchedness pressing so unjustly on the majority of the working class."

Pope John XXIII issued an encyclical in 1961 backing free market ideas, but said that from a Catholic perspective, "the global economy serves a higher good; if the economy booms, but human dignity suffers, the result is unmistakably evil."

Pope John Paul II, known for his strong anti-communist feelings, issued an encyclical in 1989 warning capitalist nations against letting the collapse of communism "blind them to the need to repair injustices in their own economic system."

Pope Benedict, whose resignation in February opened the way for Francis to head the church, issued an encyclical in 2009 that called for a world political body to manage the global economy—as well as for more government regulation to pull the world out of the Great Recession.

(Read more: Arrested Vatican prelate acted as private banker, document says)

"Pope Francis speaks in continuity with all the popes that spoke about economic issues," said Mary Catherine Sommers, a professor of philosophy at the University of St. Thomas.

"The church doesn't choose economic systems any more than political systems around the world but it does keep an eye on human systems," Sommers said.

Michael Bellafiore, a Jesuit priest and professor of theology at the University of Scranton, said Francis and the church have a role to play in shaping the business world.

"The church's task is to form consciences," Bellafiore said. "As such, corporations, banks, unions, investors all have to rise above their immediate interests and compromise. Pope Francis can promote leadership in the worst economic crisis since the Great Depression."

Attacked as socialist

For his comments, Francis has been derided as a socialist by conservative economists. And not all Catholics share the same enthusiasm for his thoughts.

"Personally, I’m much more market friendly, as was John Paul II," said Bill Donohue, president of the Catholic League, an anti-defamation group based in New York.

"I certainly applaud him for recognizing that unrestrained capitalism needs more order," Donahoe said. "If he's emphasizing we can't forget the poor, I'm all for that. But if he's leaning toward a more liberation theology, the more socialist model, which I don't think he is, then I'm against it."

"A lot of Catholics won't like what he says about economics," Schmalz said. "That includes the bureaucracy in the Vatican, which tends to be conservative on moral and economic issues."

"He's called for reforms with the Vatican bank and he's rejecting the rich cars and living quarters popes have used in the past," Schmalz said. "But how far he can go with the church remains to be seen."

(Read more: Pope says Vatican bank must be 'honest and transparent')

Francis likely to keep talking

Whether Francis can influence economic decision-making remains uncertain. Haley, of the University of New Haven, said he could use the full force of the church.

"If Francis is serious about this, he could use the Vatican's diplomatic corps to lobby various governments to come up with plans to deal with the world's economic woes," Haley said.

Unlike other popes, Francis has an advantage others didn't, Pastore said.

"Social media and media in general help him get his message out to a global public and he's being noticed because of that," Pastore said. "But what he needs to do is get folks who are capitalists to join the conversation."

—By CNBC's Mark Koba. Follow him on Twitter @MarkKobaCNBC.