Just weeks before Turkey’s early elections on Nov. 1 , Ms. Merkel came to Istanbul to meet with Mr. Erdogan and strike a deal: If Turkey helped stem the flow of refugees into Europe, Germany would help push forward talks on Turkey’s membership in the European Union. Many people fear that Ms. Merkel offered another compensation in exchange for help on the refugee issues: The European Union would tolerate Turkey’s human rights violations and its reckless handling of the Kurdish conflict.

The United States, which has crucial air bases in Turkey, cannot afford to alienate the Erdogan government, either. When Vice President Joseph R. Biden Jr. visited Turkey recently, he made a point of meeting with journalists who had been fired under government pressure. But afterward, Mr. Biden declared that the Turkish government was the United States’ “strategic partner” — an apparent gesture of reconciliation by Washington. Like many Western governments, the Obama administration has distanced itself from Mr. Erdogan since his suppression of the Gezi Park protests of 2013.

The diplomatic balancing act cannot go on indefinitely. The Syrian Kurdish group known as the Democratic Union Party, or P.Y.D., a branch of the P.K.K., is an American ally on the ground against the Islamic State and has received American military aid. Meanwhile, Turkey continues its attempt to overthrow the regime of Bashar al-Assad by supporting Jaish al-Fatah, a Syrian rebel group that includes the Nusra Front, Al Qaeda’s Syrian branch.

Turkey and the United States also do not see eye to eye when it comes to the Islamic State. Washington views the group as a high-priority threat and is pressuring Turkey to build a wall along its 60-mile border with the territory the jihadist group controls. Ankara, by contrast, sees the Islamic State as a symptom of a larger problem — Bashar al-Assad’s continued presence in Damascus — and is entreating Washington to back an Islamist-dominated rebel group. The United States is ill at ease about this state of affairs, yet believes it has no choice but to stand behind Mr. Erdogan.

Turkey and the European Union are in a more complex entanglement. At present, the European Union wields considerable leverage over Turkey, both as the market for more than 40 percent of its exports and as the arbiter of its long-stalled membership bid. Europe’s current strategy of placating Mr. Erdogan for the sake of its own short-term interests is misguided. As the Paris and Istanbul attacks have shown, Europe and the Middle East are part of one open system: Chaos and conflict in one region is sure to have repercussions in another. The millions of Syrians seeking refuge in the West, as well as the thousands of jihadists going to Syria from Europe, are now Europe’s problem — a problem that cannot be solved by building walls.