The proliferation of religious ideology and power—a phenomenon sweeping the globe from Baghdad to Rome, Tehran to Jerusalem, Kabul to Washington—is elevating “ordinary” conflict to a spiritual and apocalyptic level that deepens its potential destructiveness. How can we lower the temperature? Or, put differently, how can we undermine the rhetoric of civilizational clash and neutralize intolerant radicals?

The world requires a “religious offensive” that doesn’t give offense. Our secularist foreign-policy establishment has traditionally ignored religion in the futile hope that it would go away. But the Muslim world, from West Africa to Southeast Asia, is grounded in religion. If meaningful alliances are to be made among societies that have recently clashed or harbor historic resentments, religion—like it or not—must play a central role. And no bridging of people could be more effective than a Muslim-Catholic alliance.

The hard-bitten cynic may think this is insanity—fostering an “alliance” between religions that have been virulent sources of intolerance and global conflict. But such pessimism is misplaced. Muslims and Roman Catholics comprise the two largest religious communities in the world, each with more than a billion followers. These communities are internally plural, gifted with untapped resources for conflict resolution and violence reduction, and struggling to find a modus vivendi with one another and with the so-called secular world. They are not inevitable obstructionists to progress; those who insist so are trapped in their own tired stereotypes. Building long-term professional, personal, and institutional relationships between Muslim and Roman Catholic scholars, public intellectuals, and religious leaders constitutes a difficult but necessary task.

The partnership could begin...