IRBIL, Iraqi Kurdistan — Whatever happens in Iraq, we must try to limit the terrible fallout from the war. The place to start should be with our indispensable NATO ally Turkey, the front-line state of the post-Cold War era, whose relations with America have deteriorated dramatically in the past six years.

The immediate issue is raids by Kurdish terrorists across Turkey’s border with Iraq, which divides an area inhabited on both sides by Kurds who have long felt that they deserve their own country. Despite centuries of enmity, rapprochement is in the long-term interests of both Turkey and the Kurds of northern Iraq. But such an effort would be controversial and could be undertaken only with strong American encouragement.

First, some essential background from Irbil, the capital of Iraqi Kurdistan, which I am visiting after talks with Turkish leaders in Ankara. This peaceful city is disorienting: Am I in war-torn Iraq or booming Kurdistan? Will Irbil eventually become the capital (or part) of an independent Kurdistan? Or will this region become a battleground for another war, this one between Kurds and Turks?

You can call this place Kurdistan, as its citizens do, or northern Iraq, as the Turks do. But either way, the overwhelming majority (98% in a 2005 referendum) of its 4 million people do not want to remain part of Iraq. Who can blame them? Nothing here feels like the Middle East. The Iraqi national flag is banned; only the Kurdistan flag flies. And although the Kurds are sending some of their famously fierce warriors to Baghdad to support the Americans, they fear that General David Petraeus’ plan to turn the tide in Baghdad will not succeed.

Ever since a nation called Iraq was carved out of the debris of the Ottoman Empire by Winston Churchill and Gertrude Bell at the Cairo Conference of 1921, Turkey and Iran have opposed independence for the Kurds of northern Iraq because both fear that an independent Kurdistan on their borders would encourage existing separatist movements among their large Kurdish populations.

This symmetry of fears has led to semi-secret discussions and even some cooperation between our NATO ally and that charter member of the “axis of evil” on dealing with the PKK, a terrorist group that has conducted raids against both Turkey and Iran from bases just inside northern Iraq for many years. I would not rule out limited Turkish military action against some of those bases — especially since Prime Minister Erdogan is under enormous political pressure to show strong nationalist credentials against hawkish rivals in an election year.

After years of mishandling relations with Turkey, last year the administration appointed retired General Joe Ralston, the universally respected former NATO commander, as special envoy for the PKK problem. Mr. Ralston’s intervention helped avoid a Turkish attack in Iraq last summer, and he is accelerating his efforts to get Irbil to rein in the PKK.

But there is a larger issue: the final status of Kirkuk, the multiethnic city that sits in the middle of a huge oil field and lies just outside the official boundaries of Iraqi Kurdistan. The new Iraq Constitution calls for a referendum this year on whether Kirkuk is to be incorporated into the Kurdistan region. The Turks — who refer repeatedly to the dangers to the Turkmen, their ethnic cousins who live in Kirkuk — have said that they will not accept such an event. Avoiding a full-blown crisis will require intense mediation by America; unfortunately, Ralston’s current mandate does not include Kirkuk.

Despite their history, Turkey and Iraqi Kurdistan need each other. Kurdistan could become a buffer between Turkey and the chaos to the south, while Turkey could become the protector of a Kurdistan that, though still technically part of Iraq, is effectively cut loose from a Baghdad government that may no longer function. In addition, Turkey has a major economic opportunity in northern Iraq; already, more than 300 Turkish companies and substantial investment are a primary engine of Kurdish growth.

Rapprochement would require major undertakings by both sides. The legendary Kurdish leader who is now president of the Kurdish regional government, Massoud Barzani, needs to rein in the PKK and pledge not to interfere in Turkey’s internal affairs. A compromise that took into account legitimate Turkish concerns would be necessary on Kirkuk; while this would be difficult, especially for the Turkish military, I believe it needs to be attempted, with strong American encouragement.

History and myth make a Turkish-Kurdish deal extremely difficult. It takes visionary leaders to alter the stream of history. Charles de Gaulle and Konrad Adenauer did it for France and Germany. Nelson Mandela did it in South Africa. But such people are very, very rare. Still, the crisis in Iraq requires Turks and Kurds to think of their common interest. Having just talked to the impressive leaders of both sides, I believe they understand that they face not just a crisis but an opportunity.

Mr. Holbrooke, a former U.S. ambassador to the United Nations, writes a monthly column for the Washington Post.