Flanked by senior military commanders, Prime Minister Haider al-Abadi of Iraq on Monday announced the defeat of the Islamic State in Mosul. The bloody, nine-month reconquest of Iraq’s second-largest city after three years of occupation by the terror group was achieved thanks to close military cooperation between our Kurdish pesh merga forces and the Iraqi Army.

But there are still large areas of the country where the Islamic State is dug in, and much remains to be done. For the Kurds, the partnership with Iraqi forces makes a long-overdue political reckoning necessary and urgent.

This is why Iraqi Kurdistan will take the important step of holding a referendum on independence on Sept. 25. We believe this vote will give us a mandate to pursue a negotiated settlement with Mr. Abadi — and political recognition from his government is paramount.

The outcome of an agreement between Erbil, the capital of Iraqi Kurdistan, and Baghdad, the Iraqi capital, will have repercussions far beyond our borders. The hope of the United States administration for a second, moderate Iraqi government in 2018 relies on buy-in from both the Kurds and the Iraqis.

Washington’s default position has been that a unified Iraq within its current borders offers a viable future for the country. That view needs to be overhauled. This failed policy has threatened the very fabric of our societies, both within and beyond Iraq’s borders, fueling repression at home and conflict abroad. Washington should now encourage Baghdad to negotiate with Erbil, to achieve a realignment in the region on our own terms that can shape bilateral relations between Iraq and Kurdistan.

This would be the culmination of decades of struggle for Kurdish self-determination. My own journey along this road began in March 1991. It was a day that should have brought regeneration for the Kurds of Iraq after an uprising against Saddam Hussein; instead, panic spread through my hometown, Zakho, in Iraqi Kurdistan. As I walked home beside my mother that spring evening, the sound of a nearby explosion sent us dashing for our neighbor’s bomb shelter.

Each year, I revisit that moment in the dark underground retreat filled with shaken mothers. Later that night, my family squeezed into a truck carrying dozens of others to the nearby foothills for a five-day trek to refuge from Saddam Hussein in Turkey. That journey on foot across the snow-covered mountains of northern Iraq remains seared in my memory.

A century after the breakdown of the Ottoman boundaries, Iraq remains a forced union of peoples whose national aspirations and sense of identity have been suppressed. Members of my family spent decades in exile from successive Iraqi governments that, since the turn of the 20th century, butchered generations of Kurdish men, women and children who struggled to find their place in this artificial state.

Thus there has always been a lingering, unresolved question of identity for the Kurds of Iraq. That identity will finally achieve resolution when the people of Iraqi Kurdistan vote in the referendum. This expression of popular will should not only close a long chapter of grief but also bring new certainty and stability to an increasingly volatile region plagued by sectarian conflict and bloodshed.

Inside Iraq, a vote for independence will reconfigure the relationship with Baghdad as a just agreement between two sovereign nations. In the past, the forced unity with Baghdad crippled our efforts in the fight against the Islamic State. Even as the extremist group overran the country, Baghdad continued to lobby against Western support for the Kurds.

This foolish expedient put us all at risk. It created an absurd situation in which the central government funneled billions of dollars for the administration of services in territory held by the Islamic State even as it suspended the Kurdistan Regional Government’s share of the national budget. Rather than come together to defeat a common existential threat, Baghdad blocked licenses for nonlethal equipment and armored vehicles for Kurdish security forces, further feeding ingrained resentments.

I saw the lifesaving difference that night-vision goggles could make for pesh merga sentries facing unseen adversaries in Mosul. By contrast, Baghdad’s Shiite militias were armed to the teeth with American gear, and their veterans receive state benefits.

In December 2016, I was part of a high-level Kurdish delegation that visited the White House to discuss our national aspirations. During a passionate exchange, we were asked to delay our dream of statehood for the sake of Iraq’s war against the Islamic State. We have heard this argument before, many times.

In 2003, we agreed to American requests to give the state of Iraq a chance. Since then, Baghdad’s failure to keep its promises of genuine partnership together with greater autonomy has hardened our resolve. We reject the premise that our independence would destabilize the country. The state of Iraq is prone to instability; the crises that threaten to tear it apart at the seams will not end with the Islamic State’s defeat. The country’s polarized political system, which is characterized by the privileged position of its Shiite leadership, will endure, leaving minorities, including Iraqi Sunnis, marginalized. It was precisely this toxic political space that allowed the Islamic State to emerge.

In the next six months, the Islamic State will be militarily defeated in Iraq. But rather than a repeating of past mistakes, the war’s imminent end should lead to a realistic assessment in Erbil, Baghdad and Washington about the country’s inevitable next chapter. Although we have differences on borders, an agreement in principle to live alongside each other as two independent states would be a meaningful start.

This move would not change Iraq’s fragile borders. It would instead formalize a relationship with Baghdad and our neighbors on an equal footing to define economic, security and trade terms. And just as neither Erbil nor Baghdad interfered with Iran’s recent elections or Turkey’s referendum, we expect those countries to recognize that this is a decision for Iraq and its peoples.

The risk of sticking with a broken model is considerable. But a return to the unending conflict to which Iraq has been condemned for much of the past century is not an option. The Kurds are tired of war. We want to live in peace, alongside neighbors governed by shared values and the rule of law.