Pope Francis waded into the Israeli-Palestinian conflict on Sunday — and that may be the most exciting thing that's happened in the Mideast peace process since Bill Clinton's promising Camp David Summit in 2000 broke down with no agreement, amid mutual recriminations between Palestinian leader Yasser Arafat and Israeli Prime Minister Ehud Barak.

Now, perhaps it seems unlikely that the leader of the Roman Catholic Church can broker the end to one of the world's most intractable conflicts, between Jewish Israelis and Muslim Palestinians (primarily). After all, Pope Francis is the head of state of a sovereign city-state of about 800 people, and head of a religion that doesn't exactly have a historically amicable relationship with either Jews or Muslims.

But there's reason to be hopeful.

On Sunday, Palestinian President Mahmoud Abbas and Israeli President Shimon Peres met at a garden in the Vatican, prayed together, laughed together, hugged each other, and planted an olive tree with the pope and Patriarch Bartholomew I of Constantinople, leader of the world's Orthodox Christian churches. This feat of diplomatic acrobatics was arranged at the pope's behest in about two weeks, during which Israeli Prime Minister Benjamin Netanyahu was trying to isolate Abbas' government for forming a pact with Hamas.

Of course, there are reasons to believe this promising beginning is just another in a long line of false starts. Peres has always been more amenable to negotiating than Netanyahu; the prime minister shut down back-channel talks between Abbas and Peres in 2011, Peres said in a recent TV interview. And even if Peres had real authority to negotiate, he's leaving his largely ceremonial office at the end of June. On top of all that, the Holy See has a tiny diplomatic corps and approximately zero carrots to offer either Israel or Palestine, and few sticks.

Still, it's time for something new. The Mideast peace process has been mediated by the U.S. since at least the Camp David Accords in late 1978, with some nominal help from former British Prime Minister Tony Blair and a trio of other players: the European Union, Russia, and the United Nations, since 2002. Diplomacy takes time, but this tony-sounding Quartet paradigm doesn't seem to be making much progress. The U.S. is seen as too pro-Israel, Europe is seen as too antagonistic toward Israel's occupation, the U.N. is seen as too powerless, and Russia has been allied with the Palestinians since the Cold War.

The Vatican isn't exactly neutral when it comes to the status of Jerusalem or security in Bethlehem. Its main concern — other than world peace, of course — is the region's Christian population and access to and preservation of many of Christianity's holiest sites. That's something different for a mediator. When Pope Francis talks about wanting peace between Israel and Palestinians, most people will take him at his word: Making peace is in his job description, and in his choice of namesake.

What about the religious tensions, historical and present-day, among Christians and Jews and Muslims? The Israeli-Palestinian conflict isn't as much about religion as it is about land — the two have been intertwined since God promised Moses and the Israelites a piece of choice honey-and-milk-flowing real estate in the book of Exodus. But there is a sizable religious element to the fight, and neither the U.S. nor the Quartet is equipped to deal with that aspect.

"With the Middle East often torn apart by religious disputes, it may seem a fool's errand to seek prayers for peace from the region's three major religions, Judaism, Christianity, and Islam," says The Christian Science Monitor in an editorial. But the "humble pleas of faith at the Vatican are a welcome alternative to other attempts to bring peace to a troubled region":

One purpose of prayer is to open the heart of an individual to others, an act of love that mirrors God's love. From that, listening begins. Then dialogue and perhaps a mutual recognition of each other's fears and hopes. In the case of Israelis and Palestinians, a faith-based dialogue can ease tensions by reducing ignorance and stereotypes. It can lead to more people-to-people exchanges and bring moderation in negotiations toward a peace settlement. [Christian Science Monitor]

The main outlines of a two-state solution to the land part of the conflict have been on the table for at least 15 years. Everyone knows that Israel will come out ahead, since possession is nine-tenths of the law and the Palestinian Authority has no army, no sovereignty in any real sense of the word, and no particularly powerful advocate on the world stage. The question is how much, and how to get to an agreement.

Lisa Goldman argues that neither side really has any incentive to bridge the final gaps, but that seems a little overly cynical. Both Israel and Palestine would benefit from being two peacefully coexisting states, even if certain parts of each country (Israeli settlers and Hamas militants, for example) wouldn't. She's probably right, however, that it's time for the U.S. to step aside as the conflict's main peace broker.

What could Pope Francis bring to the table? He's popular; he's reasonably neutral; he's from Argentina, a country that hasn't played a part in Israel-Palestinian peace talks; and he's new to the process himself. Also, he believes in miracles.

Is that enough to nudge Netanyahu and Abbas, plus their governing partners, to a peace deal? "We have no presumptions that this event will bring peace," says Rev. Pierbattista Pizzaballa, the Vatican's custodian of holy sites in the Holy Land. "The pope does not want to get into the political questions of the Israeli-Palestinian conflict." But Pizzaballa, along with having a great name, also gets to the central truth of the pope's new role in the peace process.

A Mideast prayer session at the Vatican is "an invitation to politicians to pause and look heavenward," Pizzaballa tells Religion News Service. "Everyone wants something to happen, something to change. Everyone is tired of these eternal negotiations that never end." As the pope might say: Amen.