Wreckage lies on the ground in front of a Turkish millitary station covered by a tarpaulin after a suicide atack on Aug. 2 in eastern Turkey. (Agence France-Presse via Getty Images)

LESS THAN two weeks after Turkey and the United States announced stepped-up cooperation to fight the Islamic State, the initiative is in danger of being undermined by a parallel war. Turkish planes have been pounding camps of the Kurdistan Workers’ Party (PKK) in southeastern Turkey and northern Iraq, and the PKK has responded with attacks on security forces, leaving a two-year-old cease-fire in ruins. While the United States regards the PKK as a terrorist group, the fighting threatens to weaken the alliance against the Islamic State unless it can be quickly ended.

Turkish officials say they launched the offensive in response to the breaking of the cease-fire by the PKK — which, in turn, blamed Turkey for allowing a devastating suicide bombing last month that killed dozens of Kurdish activists. In truth, Turkish President Recep Tayyip Erdogan appears to have powerful motives for targeting the Kurdish group. A Syrian Kurdish force allied with the PKK has been gaining ground from the Islamic State along the Turkish border, aided by U.S. airstrikes. While that has curtailed the jihadists’ access to Turkey, it has also raised Ankara’s fears of a new Kurdish ministate emerging on its southern frontier, near the Kurdistan autonomous region in northern Iraq.

The de facto safe zone in northern Syria that the United States and Turkey agreed to establish would have the benefit, for Turkey, of preventing Syrian Kurds from expanding their domain westward. Meanwhile, the assault on the PKK could advance Mr. Erdogan’s domestic political ambitions. In June, the autocratically minded president saw his hopes of rewriting Turkey’s constitution thwarted, or at least delayed, when his ruling Justice and Development (AK) Party failed to win a parliamentary majority, much less the supermajority it needs to change the constitution.

The principal agent of Mr. Erdogan’s defeat was the Kurdish Peoples’ Democratic Party, a liberal group linked to the PKK that attracted support from secular Turks who oppose Mr. Erdogan’s attempted concentration of power. Many Turkish analysts believe Mr. Erdogan is hoping to call a new election for November; he may calculate that war with the PKK will drive down the Kurdish party’s support. Any losses it suffered would probably mean additional seats for Mr. Erdogan’s party, allowing it to regain its majority.

Every part of this strategy should be troubling for the Obama administration. U.S.-Turkish relations have already deteriorated in recent years as Mr. Erdogan has eroded the country’s democracy through attacks on the media and civil society; his Putinesque initiative to rewrite the constitution would compound the damage. At the same time, Kurdish forces in Iraq and Syria have emerged as the most effective ground combatants against the Islamic State and the best U.S. allies in the region. Though the Turkish offensive has not directly touched those groups, the new conflict could poison their fragile relations with Turkey and complicate further military action against the jihadists.

The best U.S. response is to urge Mr. Erdogan to quickly end the offensive against the PKK and seek a new cease-fire. In a Post op-ed last week, Prime Minister Ahmet Davuto ğlu asserted that a long-standing peace process was not dead and that he was “determined to take it forward, as rapidly as I am able.” He should be held to that pledge.