Since the Islamic State began seizing significant amounts of territory in northern Syria and Iraq, policy makers and analysts have focused primarily on the question of whether America should arm the Kurds to fight the jihadi group.

But this debate overlooks a key flaw in America’s Kurdish policy: while military support for the Kurds in Iraq and Syria has increased, the development of a corresponding political road map to deal with Kurdish entities in the region has lagged behind. Washington’s exclusive focus on enabling the Kurds to fight the Islamic State risks creating new problems that could plague Iraq and Syria for much longer.

The United States has come to believe it faces a dilemma: It needs to arm the Kurds to fight the Islamic State, but it is wary of kindling the Kurds’ political expectations.

In order to fight the Islamic State along a long front line in Syria and Iraq, America needs help from Kurdish forces in both countries. To this end, it has provided military support to the Kurdistan Regional Government in Iraq and coordinated airstrikes with the dominant Kurdish armed force in Syria, the People’s Protection Units, or Y.P.G.

Meanwhile, the Obama administration has been hesitant to strengthen the semi-autonomous institutions of the Iraqi Kurdistan region, largely out of concern that these could one day be the building blocks of Iraqi Kurdish independence. Even American military assistance has benefited Kurdish forces affiliated with specific political parties rather than the region’s integrated military institution as a whole. That’s because the United States and many of its regional allies worry that a Kurdish breakaway from Iraq would invite greater unpredictability and chaos, including by stoking similar separatist sentiments among Kurdish populations in neighboring countries, thereby risking the collapse of the regional order.

In reality, however, independence is a highly unlikely scenario for reasons that have little to do with American policy. These include entrenched divisions among Iraqi Kurds and growing Kurdish dependence on regional powers like Iran and Turkey that reject the idea of Kurdish independence outright. Although independence remains an emotionally powerful aspiration among many Kurds it has in practice become more of a political card for some Iraqi Kurdish leaders to play than a viable political project.

The United States has been careful not to jeopardize its strategic relationship with Turkey. It has only been willing to risk Turkey’s ire for one reason: to aid the Y.P.G. in its fight against the Islamic State. Last week, the American military reportedly airdropped 50 tons of ammunition to forces, including many Y.P.G. fighters, in northern Syria. While arming these Syrian Kurds, Washington has shied away from engaging diplomatically with the Y.P.G.’s political branch, the Syrian Democratic Union Party, or P.Y.D. (Turkey views the P.Y.D. as a potential threat due to its ties with the Kurdistan Workers’ Party, or P.K.K.)

The problem with bolstering the Kurds’ military strength without a parallel political initiative is that America hasn’t set clear restraints on what the Kurds can do with their newfound strength or offered them guarantees of what they can expect in the future. This has reduced America’s ability to influence its Kurdish allies, even as they stretch beyond their traditional frontiers.

In Iraq, Kurdish forces have moved into ethnically mixed territories, where they now exercise de facto control. Knowing that American military support comes with only one string attached — fighting the Islamic State — Kurdish fighters have hastily established control on the ground. They have used their military advantage to subordinate local non-Kurds in Kirkuk and other disputed territories, sowing feelings of mutual distrust and revenge.

In northern Syria, Kurdish forces have worked fast to consolidate their control with the aim of positioning themselves as unavoidable players in the future of the country. However, the Kurds’ advances into areas that are not predominately Kurdish have provoked enmity from other groups. The Syrian government’s old narrative, which brands all Syrian Kurds as “separatists,” is now being echoed by non-Kurdish opposition groups fighting against the regime of Bashar al-Assad.

America’s exclusive military focus has encouraged the Kurds to invest disproportionately in their military achievements. This approach has alienated non-Kurdish populations who now live under Kurdish rule, while increasing intra-Kurdish competition for access to foreign military support. The P.Y.D., for instance, may now seek to strike up a relationship with Russia or use the prospect of such a partnership as leverage to acquire greater American military support. All of this makes Washington’s immediate goal of pulling together a coordinated fight against the Islamic State and the longer-term goal of removing the conditions that allowed the group to arise ever more elusive.

Military assistance to the Kurds must be combined with a clear political roadmap. At a minimum, this would mean an American commitment to develop Iraqi Kurdish institutions and help mediate budget and oil disputes with Baghdad, which would provide some critical guarantees to the welfare of the Kurdish region.

Washington could provide such support in return for the Kurds’ agreeing to establish joint security and administrative arrangements with local non-Kurdish actors in the disputed territories.

In Syria, the United States should match its military support for the Y.P.G. with political engagement of the P.Y.D. In return, the Syrian Kurds could pledge to address Turkish concerns by distancing themselves from the P.K.K.’s fight against Turkey. To do this, the P.Y.D. and Y.P.G. would need to implement previous cooperation agreements with Iraqi Kurdish groups that have strong relations with Turkish government and to share decision-making power with Arab opposition factions backed by Turkey. All of this would give Washington more influence over Syrian Kurdish forces before they push further into mixed or non-Kurdish areas.

America must stop dealing with the Kurds strictly as military allies. Otherwise, Washington could end up contributing to precisely the sort of regional instability that its policy is intended to prevent.

Originally published in The New York Times.