(CNN) -- U.S. President Barack Obama and Pope Francis met for the first time Thursday at Vatican City.
The two world leaders greeted each other with a smile and a handshake, and posed for pictures before sitting down across a table from each other.
The tete-a-tete was an opportunity for a reset of sorts between the Obama administration and Catholic leadership following several years of strained relations.
The goal: focus on areas where two of the world's most influential men agree and gently tread ground where they differ.
That means the President and the Pontiff will, as the White House said in a statement, focus on "shared commitment to fighting poverty and growing (income) inequality" and gingerly navigate such thornier topics as same-sex marriage, contraception and abortion.
"In general, they'll be looking for areas of conversation where there is great agreement between the Vatican and the administration," said Steve Schneck, director of the Institute for Policy Research and Catholic Studies at the Catholic University of America.
"The Pope will likely bring up immigration in a broad way ... and I do think there's a possibility the bishops' concerns about contraception in the (Affordable Care Act) might be mentioned," Schneck said.
The meeting takes place two days after the U.S. Supreme Court heard arguments on a contraception mandate included in the President's signature health care reform law.
While the law exempts churches and houses of worship from the requirement, nonprofit, religiously affiliated groups are required to either directly provide contraception coverage to their employees or do so through a third-party insurer.
The U.S. Conference of Catholic Bishops has been vocal in its opposition to the provision, said Sister Mary Ann Walsh, a spokeswoman for the organization.
"Religious liberties and right-to-life issues are a concern," she said of the tension between American Catholic leadership and the administration. However, "the U.S. Bishops have appreciated the administration's cooperation on issues of mutual concern."
Those areas of "mutual concern" include immigration and poverty -- issues where the President and the Pope could find common ground.
Francis underscored his commitment to the plight of immigrants during a trip to the Italian island of Lampedusa last year, a place where thousands of African migrants desperately fleeing political upheaval and poverty pour onto European shores. Many die in the attempt to cross.
Next month, a group of American Catholic leaders, including Cardinal Sean O'Malley, the archbishop of Boston, will follow suit and travel to the U.S.-Mexico border in order to highlight immigration concerns.
On Wednesday, the day before Obama's meeting with the Pope, the administration renewed its public call for immigration reform by backing an effort by House Democrats to force a vote on the matter.
"Immigration reform is the right thing to do for our economy, our security, and our future," the White House said in a statement.
Tensions between the administration and many leaders in the American Catholic community began early in the President's tenure over his support for abortion rights.
A number of bishops criticized the University of Notre Dame's decision in 2009 to award Obama an honorary law degree and invite him to give the commencement address.
Relations frayed further over abortion funding in Obamacare, leading the U.S. Conference of Bishops to pan the law.
"It was a very tough year," said Christopher Hale, a senior fellow with Catholics in Alliance for the Common Good who helped lead national Catholic outreach for Obama's 2012 re-election campaign. "It was hard to find any reasonable Catholic who thought the Health and Human Services mandate was handled well."
Differences over same sex-marriage only added to the tense relationship.
Francis will likely not wade into politically charged conversations during the meeting, religion experts say.
"The Vatican has to be very careful to not create a gap between what they're saying and the bishops are saying," Schneck said. "They will be very careful not to undercut the American bishops in that regard."
The meeting with Pope Francis, whose approval ratings are in the high 80s, might also boost Obama in that regard. His standing with the public has hovered in the low 40s.
After all, the Pope's name and quotes have been invoked in everything from discussions over unemployment insurance, the minimum wage and the bigger issue of income inequality.
"If I was advising President Obama, I would say the number one spokesperson on American immigration reform should be Pope Francis," Hale said. "He has so much capital in this city. You have Catholics, Jews and Atheists on the Hill quoting him."
House Speaker John Boehner, an Ohio Republican and a Catholic, recently invited the Pope to address a joint session of Congress.
"Everybody on the planet would like to have their picture taken with the Pope these days," Schneck said. "One of the things that would delight Obama is if some of that popularity would rub off. Given the President's current low numbers, he is hoping for a bit of a boost."
CNN's Ed Payne contributed to this report.
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