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A year after becoming Iraq’s prime minister, Mustafa al-Kadhimi has begun to apply lessons from his country’s history of wars and divisions to the rest of the Middle East. In recent weeks, he has become a pivotal mediator in breakthrough talks between Iran and Saudi Arabia.

As someone who once led a foundation dedicated to conflict resolution, Mr. Kadhimi wants to end the competition between the region’s two giants – a zero-sum competition often played out violently in Iraq’s internal conflicts.

The initial talks began in Baghdad a month ago, focused mainly on stopping a proxy war in Yemen. Progress on that front could lead to a wider detente. Any further dialogue between Iran and Saudi Arabia, which broke off ties five years ago, still needs a trusted go-between. That is where Mr. Kadhimi’s experience in trying to reconcile Iraq’s own differences could pay off in bringing peace to the neighborhood.

His selection as prime minister a year ago was a result of elected leaders in Baghdad responding to street protests aimed at ending the factional fighting that has hurt Iraq’s fragile democracy. Mr. Kadhimi’s background includes setting up the Iraq Memory Foundation, which chronicles the suffering of Iraqis under dictator Saddam Hussein. He also led the Humanitarian Dialogue Foundation, which worked to reconcile differences between Iraq’s majority Shiites and minority Sunnis.

As prime minister, his mediating skills have yet to solve Iraq’s deep divisions. Just holding fair elections later this year is proving to be big task.

 Mr. Kadhimi does not have a political party of his own. But he and other leaders now realize Iraq must first end the contest between Iran and Saudi Arabia that spills over in Iraq. Their timing is right. Both Iran and Saudi Arabia are under domestic and international pressure to cool their antagonism and focus on their economies.

“Iraq is capable of playing the role of mediator in the region rather than being a source of instability,” said Iraqi President Barham Salih in a recent talk. “The Middle East has been condemned to a cycle of conflict and instability over the last few decades. ... It’s time to move beyond.”

But first, a bridge of trust between Iran and Saudi Arabia must be built. The first stone has been put in place, thanks to an Iraqi leader who has learned from the suffering of his own people.