A Kurdish man’s house is riddled with bullet holes after armed clashes between the PKK and Turkish armed forces on Jan. 10. (Refik Tekin/European Pressphoto Agency)

PHOTOGRAPHS OF black smoke rising from a dense thicket of concrete buildings have by now become a painfully familiar emblem of ongoing wars in Syria and Iraq. So it’s perhaps less shocking than it should be that such images are now appearing from the cities of Turkey, a NATO member as well as a country thought to be one of the last anchors of order in a tumultuous region. With little international notice, the government of Recep Tayyip Erdogan is engaged in a full-scale military campaign against ethnic Kurdish militants that has killed thousands, displaced hundreds of thousands and left parts of several large towns in ruins.

The Kurdish population under siege is not to be confused with that of northern Iraq or northern Syria, where Kurdish forces backed by the United States and other Western governments are fighting the Islamic State and carving out their own autonomous areas. The target of Mr. Erdogan’s offensive are Turkish citizens who live in the southeastern part of the country, where Kurds often are the majority ethnic group. In 2002, after first coming to office, Mr. Erdogan promised to end long-standing repression of the minority; he struck a cease-fire and opened negotiations with the Kurdistan Workers’ Party (PKK), an armed insurgent group.

That fragile detente unraveled last summer, not long after a Turkish political party supported by Kurds, the Peoples’ Democratic Party, won more than 10 percent of the vote in elections for parliament, denying Mr. Erdogan’s ruling party a majority. A Kurdish political rally was bombed, apparently by the Islamic State; blaming the government for failing to prevent it, the PKK carried out an attack on security forces. It has since dug into at least seven towns with a total population of more than 1 million.

The government has placed those urban areas under curfew, and both sides are using heavy weapons, including rocket launchers and mortars. Mr. Erdogan brags of having killed more than 3,000 militants. Last week the military said 225 PKK fighters had been dispatched in a neighborhood of Diyarbakir, a large city, and a nearby town in the last three weeks alone. The true scale and results of the fighting are difficult to judge, as the government has excluded journalists from the area and intimidated Turkish media.

Two conclusions are nevertheless easy to reach: Mr. Erdogan will never succeed in eliminating by force the PKK or Turkish Kurds’s aspirations for more autonomy, and by prosecuting his campaign he is impeding the fight against the Islamic State. Western governments have shied from pressuring the Turkish strongman about the offensive because they still count on his cooperation on multiple fronts, including in preventing refu­gee flows from Syria and allowing U.S. warplanes to operate from Turkish bases. But Mr. Erdogan needs to be pushed toward reopening negotiations with Turkish Kurdish leaders. A settlement that grants the Kurds and their communities more political rights is an essential component of what must eventually be a broader solution for Kurdish aspirations in the region.